We provide mensuration practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on mensuration skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of mensuration Questions

Question No | Questions | Class |
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1 | Find the measure of all the angles of a parallelogram, if one angle is ( 24^{circ} ) less than twice the smallest angle. A ( cdot 68^{circ}, 112^{circ}, 68^{circ}, 112^{circ} ) B . ( 48^{circ}, 72^{circ}, 48^{circ}, 72^{circ} ) c. Insufficient data D. None of these | 8 |

2 | A copper wire is in the form of a circle with radius ( 35 mathrm{cm} ). It is bent into a square. Determine the side of the square. | 8 |

3 | A square ( A B C D ) is divided equally into 5 rectangles. The perimeter of each rectangle is ( 60 mathrm{cm} . ) Find the perimeter of the square. A. ( 120 mathrm{cm} ) B. ( 100 mathrm{cm} ) c. ( 25 mathrm{cm} ) D. ( 60 mathrm{cm} ) | 8 |

4 | A table cover ( 6 m times 3 m ) is spread on a table top. If ( 25 mathrm{cm} ) of the cover hangs all around the table then the cost of polishing the table @ Rs ( 12 m^{2} ) is A . ( R s 165 ) B. ( R s 175 ) c. ( R s 180 ) D. ( R s 195 ) | 8 |

5 | A farmer wishes to start a 100 square metres rectangular vegetable garden. since he has only 30 metres barbed wire, he fences three sides of the rectangular garden. The ( 4^{t h} ) side of the garden is surrounded by the compound wall of his house. The dimensions of the garden is ( mathbf{A} cdot 25 mathrm{m} times 4 mathrm{m} ) B . ( 25 mathrm{m} times 5 mathrm{m} ) c. ( 20 mathrm{m} times 5 mathrm{m} ) D. ( 20 mathrm{m} times 4 mathrm{m} ) | 8 |

6 | Two isosceles triangles have equal vertical angles and their areas are in the ratio 36: 25 Find the ratio of their corresponding heights. | 8 |

7 | f the diagonal of a quadrilateral shaped field is ( 24 m ) and the perpendiculars dropped on it from the remaining opposite vertices are ( 8 m ) and ( 13 m ) then the area of the field is | 8 |

8 | Which of the following statements are true (T) and which are false (F)? If three sides of a quadrilateral are equal, it is a parallelogram. A . True B. False | 8 |

9 | The area of rhombus is ( 119 mathrm{cm}^{2} ) and its perimeter is ( 56 mathrm{cm} . ) Find its height. | 8 |

10 | ( boldsymbol{P} boldsymbol{Q} boldsymbol{R} boldsymbol{C} ) parallelogram, ( boldsymbol{Q} boldsymbol{M} ) is the height form ( Q ) to ( R C ) and ( Q N ) is the height from ( Q ) to ( P S . ) If ( R C=12 mathrm{cm} ) and ( Q M=7.6 mathrm{cm} . ) Find (a) the area of the parallegram ( P Q R C ) ( (b) Q N ) if ( P S=8 c m ) | 8 |

11 | The ratio of the length of the parallel sides of a trapezium is 5: 3 and the distance between then is 16 cm. If the area of the trapezium is ( 960 mathrm{cm}^{2} ), find the length of the parallel sides. ( mathbf{A} cdot 45 mathrm{cm} ) and ( 65 mathrm{cm} ) B. ( 35 mathrm{cm} ) and ( 75 mathrm{cm} ) c. ( 45 mathrm{cm} ) and ( 75 mathrm{cm} ) D. ( 55 mathrm{cm} ) and ( 75 mathrm{cm} ) | 8 |

12 | The area of a trapezium is 450 sq.cm and the lengths of the parallel sides are ( 37 mathrm{cm} ) and ( 23 mathrm{cm} . ) Find the distance between them. | 8 |

13 | f the volume of each cube is 1 cubic ( mathrm{cm} ) then the volume of the cuboid given in the following figure is A. 12 cubic cm B. 24 cubic cm ( c .36 ) cubic cm D. 26 cubic cm | 8 |

14 | The side of a regular hexagon is ( boldsymbol{p} boldsymbol{c m} ) then its area is A ( cdot frac{sqrt{3}}{2} p^{2} mathrm{cm}^{2} ) B. ( frac{3 sqrt{3}}{2} p^{2} mathrm{cm}^{2} ) c. ( 2 sqrt{3} p^{2} c m^{2} ) D. ( 6 p^{2} mathrm{cm}^{2} ) | 8 |

15 | The area of a parallelogram is ( y mathrm{cm}^{2} ) and its height is ( h ) cm. The base of another parallelogram is ( x ) cm more than the base of the first parallelogram and its area is twice the area of the first. Find, in terms of ( y, h ) and ( x, ) the expression for the height of the second parallelogram. A ( frac{h y}{y h-x} ) B. ( frac{y}{y-x h} ) c. ( frac{2 h y}{y+x h} ) D. None of these | 8 |

16 | A rectangular field is half as wide as it is long and is completely enclosed by ( x ) yards of fencing. The area in terms of ( x ) is A ( cdot frac{x^{2}}{2} ) в. ( 2 x^{2} ) c. ( frac{2 x^{2}}{9} ) D. ( frac{x^{2}}{18} ) E. none of these | 8 |

17 | Find the volume of a cube of edge ( 6 mathrm{cm} ) ( mathbf{A} cdot 64 mathrm{cm}^{3} ) В. ( 125 mathrm{cm}^{3} ) ( c cdot 216 c m^{3} ) D. ( 343 mathrm{cm}^{3} ) | 8 |

18 | If the volume of a cuboid is ( 880 mathrm{cm}^{3} ) and area of base is ( 88 mathrm{cm}^{2} ). Find the height. | 8 |

19 | An isosceles trapezium has two parallel sides 60 m and 40 m. If the perimeter of this trapezium is 160 m, find the length of the other two sides. 1: 1 1. n o on na nair ofannocite sides | 6 |

20 | A flooring tile has the shape of a parallelogram whose base is ( 24 mathrm{cm} ) and the corresponding height is ( 10 mathrm{cm} . ) How many such tiles are required to cover a floor of area ( 1080 m^{2} ? ) A . 45,000 B. 75,000 c. 40,000 D. 45,00 | 8 |

21 | Two adjacent sides of parallelogram are ( 24 mathrm{cm} ) and ( 18 mathrm{cm} . ) If the distance between the longer sides is ( 12 mathrm{cm} ); find the distance between the shorter sides. A. ( 9 mathrm{cm} ) B. ( 16 mathrm{cm} ) c. ( 24 mathrm{cm} ) D. Data insufficient | 8 |

22 | Area of parallelogram ( A B C D=60 c m^{2} ) then find the area of parallelogram ABEF ( A cdot 30 mathrm{cm}^{2} ) B. ( 60 mathrm{cm}^{2} ) ( c cdot 40 c m^{2} ) None of the above | 8 |

23 | A regular hexagon of maximum possible area is cut off from an equilateral triangle. The ratio of the area of the triangle to the area of hexagon will be- A ( cdot sqrt{frac{3}{2}} ) B. ( frac{sqrt{6}}{2} ) c. ( frac{3}{sqrt{2}} ) D. ( frac{3}{2} ) | 8 |

24 | The area of a rectangular garden, ABCD, is ( 100 m^{2} . ) Inside the garden there is a rectangular lawn, EFGH, whose sides are parallel to those of the garden. Find the area of the lawn, EFGH(in sq metres). A ( cdot 110-5 x-frac{200}{x} ) B. ( 110+5 x-frac{200}{x} ) c. ( _{110}+5 x+frac{200}{x} ) D. ( 110-5 x+frac{200}{x} ) | 8 |

25 | Consider the triangle OAB in the xyplane where ( 0=(0,0) A=(6,0), B= ) ( (sqrt{2}, 3) . ) A sqare PQRS is inscribed in the square with ( P, Q ) on ( O A, R ) on ( A B ) and Son BO. Then the side of the square equals A. ( 3 / sqrt{2} ) B. ( frac{9}{4} ) c. ( frac{3}{2} sqrt{frac{5}{2}} ) D. | 8 |

26 | If length of a rectangle is ( 5 mathrm{cm} ) and breadth of the rectangle is ( 12 mathrm{cm} . ) Find the area of the rectangle. ( mathbf{A} cdot 25 c m^{2} ) В. ( 60 mathrm{cm}^{2} ) ( mathbf{c} cdot 31 c m^{2} ) D. ( 12 mathrm{cm}^{2} ) | 8 |

27 | The side of a rhombus is ( 26 m ) and length of one of its diagonal is 20 m. The area of the rhombus is A ( cdot 120 m^{2} ) В. ( 240 mathrm{m}^{2} ) c. ( 480 m^{2} ) D. None | 8 |

28 | A parallelogram ( A B C D ) has sides ( A B=24 mathrm{cm}, A D=16 mathrm{cm} . ) The distance between the sides ( A B ) and DC is ( 10 mathrm{cm} . ) Find the distance between the sides ( A D ) and ( B C= ) ( mathbf{A} cdot 16 mathrm{cm} ) B. ( 18 mathrm{cm} ) c. ( 15 mathrm{cm} ) D. ( 26 mathrm{cm} ) | 8 |

29 | Find the area of the regular hexagon PQRST in which each side measures ( 17 mathrm{m} ) and its height is ( 33 mathrm{m} ) | 8 |

30 | The length of the fence of a rectangled shaped field ( A B C D ) is ( 130 mathrm{m} ) and side ( A B ) is ( 60 mathrm{m}, ) find the area of the field. | 8 |

31 | A swimming pool is ( 24 mathrm{m} ) long and ( 15 mathrm{m} ) broad When a number of men dive into the bath the height of water rises by 1 ( mathrm{cm} ) If the average volume of water displaced by each man be ( 0.1 m^{3} ) how many men are there in the bath? ( A cdot 32 ) B. 36 c. 42 D. 46 | 8 |

32 | ( P Q R S ) is a parallelogram ( P M ) is the altitude on base ( S R . S N ) is the altitude on base ( Q R ) If ( S R=8.2 mathrm{m}, P M=4.8 ) ( mathrm{m} ) and ( S N=6 mathrm{m} ). Find ( P S ) | 8 |

33 | Find the area of a parallelogram with a base of ( 200 mathrm{cm} ) and height of ( 2.5 mathrm{cm} ) в. ( 510 mathrm{cm}^{2} ) ( mathrm{c} cdot 520 mathrm{cm}^{2} ) D. ( 300 mathrm{cm}^{2} ) | 8 |

34 | Find the area of a rhombus whose side is ( 5 c m ) and whose altitude is 4.8 cm. If one of its diagonal is ( 8 mathrm{cm} ) long, find the length of the other diagonal | 8 |

35 | A hall has dimensions ( 24 mathrm{m} times 8 mathrm{m} times 6 ) m The length of the longest pole which can be accommodated in the hall is A. ( 26 mathrm{m} ) B. 28 m ( c cdot 30 m ) D. 36 m | 8 |

36 | If a wire is bent into the shape of a square, then the area enclosed by the square is ( 81 mathrm{cm}^{2} ). When the same wire is bent into a semi-circular shape, then the area enclosed by the semi circle will be ( mathbf{A} cdot 81 c m^{2} ) B. ( 44 mathrm{cm}^{2} ) ( mathbf{c} cdot 77 c m^{2} ) D. ( 154 c m^{2} ) | 8 |

37 | A land surveyor records the various treatments of a field in his measurement book as given below. The area of the field surveyed is (all reading are in meters): ( A cdot 6000 ) sq. ( m ) B. 7000 sq. ( m ) c. 7500 sq. ( m ) D. 8250 sq. | 8 |

38 | Draw parallelogram ( A B C D ) with the following measurements and calculate its area ( A B=6 c m, B D=8 mathrm{cm} ) and ( A D= ) ( 5 mathrm{cm} ) | 8 |

39 | ( A B C D ) is a quadrilateral such that ( A B=5 c m, B C=4 c m ; C D= ) ( 7 c m, A D=6 c m ) and diagonal ( B D= ) ( 5 c m, ) then the ( A(square A B C D) ) is ( 4(3+ ) ( sqrt{6}) c m^{2} ) A. True B. False | 8 |

40 | The angle of elevation of the top of a vertical tower from a point A due east of it is ( 45^{circ} . ) The angle of elevation of the top of the same tower from a point B due south of ( A ) is ( 30^{circ} ) If the distance between ( A ) and ( B ) is ( 54 sqrt{2} m ),then the height of the tower (in metres),is A. ( 18 sqrt{3} ) is B . 54 c. ( 27 sqrt{2} ) D. 108 | 8 |

41 | The area of circle if the circumference is ( 20 pi ) | 8 |

42 | n the given, ( Delta A B C ) has sides ( A B= ) ( mathbf{7} . mathbf{5} mathrm{cm}, mathbf{A} boldsymbol{C}=mathbf{6 . 5} mathbf{c m} ) and ( mathbf{B C}=mathbf{7} mathrm{cm} ) On base ( B C ) a parallelogram ( D B C E ) of same area as that of ( Delta A B C ) is constructed. Find the height ( D F ) of the parallelogram. ( 4.7 mathrm{cm} ) в. 5 ст ( c .3 mathrm{cm} ) ( 0.2 mathrm{cm} ) | 8 |

43 | Students of a school staged a rally for a cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes ( A B, B C ) and CA; where the Other through ( A C, C D ) and DA. Then they cleaned the area enclosed within their lanes. If ( boldsymbol{A B}= ) ( mathbf{9} boldsymbol{m}, boldsymbol{B} boldsymbol{C}=mathbf{4 0 m}, boldsymbol{C D}=mathbf{1 5 m}, boldsymbol{D} boldsymbol{A}= ) ( 28 m ) and ( angle B=90^{0}, ) which group cleaned more area and by how much? Find the total area cleaned by the students. | 8 |

44 | Four cubes, each of edge ( 9 mathrm{cm}, ) are joined as shown below, then the volume of the resulting cuboid is in ( c m^{3} ) | 8 |

45 | The area of a field is in the shape of a trapezium measures ( 1440 m^{2} ). The perpendicular distance between its parallel sides is ( 24 m . ) If the ratio of the parallel sides is ( 5: 3 . ) What is the length of the longer parallel side? A . ( 75 mathrm{m} ) B. ( 70 m ) c. ( 80 m ) D. ( 85 m ) | 8 |

46 | The area of the parallelogram with vertices (0,0),(2,3),(-2,3) and (-4,0) is A . 10 B. 12 ( c cdot 13 ) ( D cdot 16 ) | 8 |

47 | ( A B C D E ) is a regular pentagon. A star of five points ( A C E B D A ) is formed to join their alternate vertices. The sum of all five vertex angles of this star is A. Two right angle B. Three right angle c. Four right angle D. Five right angle | 8 |

48 | A park in the shape of a quadrilateral ( A B C D ) has ( C=90^{0} . A B=18 m ) ( B C=24 m, C D=10 m ) and ( A D= ) 16 ( m ). how much area does it occupy? | 8 |

49 | Prove that the straight line joining the mid-points of the opposite sides of a parallelogram divides it in to two parallelograms of equal area. | 8 |

50 | The diagonals of a rhombus are ( 24 mathrm{cm} ) and ( 10 mathrm{cm} . ) Calculate its area. A ( cdot 120 mathrm{cm}^{2} ) в. ( 130 mathrm{cm}^{2} ) ( mathrm{c} cdot 220 mathrm{cm}^{2} ) D. None of these | 8 |

51 | The length of two adjacent sides of a parallelogram are ( 17 mathrm{cm} ) and ( 12 mathrm{cm} ). one of its diagonals is ( 25 mathrm{cm} ) long. Find the area of the parallelogram. | 8 |

52 | The adjacent sides of a parallelogram ( 36 mathrm{cm} ) and ( 27 mathrm{cm} ) in length. If the perpendicular distance between the shorter sides is ( 12 mathrm{cm}, ) find the distance between the longer sides. | 8 |

53 | The area of a trapezium is ( 405 mathrm{cm}^{2} ). its parallel sides are in the ratio 4: 5 and the distance between them is ( 18 mathrm{cm} ) Find the length of each of the parallel sides. | 8 |

54 | Find the area of a parallelogram with base ( 32 mathrm{cm} ) and height ( 16.5 mathrm{cm} ) | 8 |

55 | The coordinates of the point which is equidistant from the three vertices of the ( Delta A O B ) as shown in the given figure ( mathbf{A} cdot(x, y) ) B . ( (y, x) ) c. ( frac{x}{2}, frac{y}{2} ) D. ( frac{y}{2}, frac{x}{2} ) | 8 |

56 | The ratio of the total surface area and the lateral surface area of a right cone is 4: 3 and its height is ( 8 mathrm{m}, ) then its base area is approx A ( cdot 24 m^{2} ) B. ( 33 m^{2} ) ( mathbf{c} cdot 21 m^{2} ) D. ( 27 m^{2} ) | 8 |

57 | The area of the parallelogram with diagonals ( 5 c m, 6 c m ) respectivelu ( mathbf{A} cdot 18 mathrm{cm}^{2} ) B. ( 27 mathrm{cm}^{2} ) ( mathbf{c} cdot 15 c m^{2} ) D. None of these | 8 |

58 | Find the area of a quadrilateral ( boldsymbol{P Q R S} ) in which ( angle Q P S=angle S Q R= ) ( 90^{circ}, P Q=12 mathrm{cm}, P S=9 mathrm{cm}, Q R= ) ( 8 c m ) and ( S R=17 mathrm{cm} ) | 8 |

59 | If one side of a rhombus has end points (4,5) and (1,1) then find the maximum area of rhombus. | 8 |

60 | A garden is 24 m long and 14 m wide. There is a path ( 1 ~ m ) wide outside the garden along its sides. If the path is to be constructed with square marble tiles ( 20 mathrm{cm} times 20 mathrm{cm}, ) find the number of tiles required to cover the path? A. 1800 в. 200 c. 2000 D. 2150 | 8 |

61 | 15. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate 100 per metre it will cost the village panchayat * 75000 to fence the plot. What are the dimensions of the plot? | 8 |

62 | 54. A wire of length 44 cm is first bent to form a circle and then rebent to form a square. The dif- ference of the two enclosed ar- eas is (1) 44 cm (2) 33 cm (3) 55 cm (4) 66 cm | 6 |

63 | Draw quadrilateral ABCD with the following measurements. Also find its area. ( A B=6 mathrm{cm}, mathrm{BC}=6 mathrm{cm}, angle mathrm{BAC}=50^{circ}, angle ) ( A C D=30^{circ} ) and ( angle C A D=100^{circ} ) | 8 |

64 | A school has a hall which is 22 m long and ( 15.5 m ) broad. A carpet is laid inside the hall leaving all around a margin of ( 75 mathrm{cm} ) from the walls. Find the area of the carpet and the area of the strip left uncovered. If the width of the carpet is ( 82 mathrm{cm}, ) find the cost at the rate of ( boldsymbol{R} boldsymbol{s} boldsymbol{6} boldsymbol{0} ) per meter | 8 |

65 | Find the edge of the cube whose volume is ( 216 m^{3} ) | 8 |

66 | Find area of parallelogram whose base is ( 24 mathrm{cm} ) and height is ( 5 mathrm{cm} ) | 8 |

67 | If ( angle B_{1} O A_{1}=60^{circ} & ) radius of biggest circle is r. According to figure trapezium ( boldsymbol{A}_{1} boldsymbol{B}_{1} boldsymbol{D}_{1} boldsymbol{C}_{1}, boldsymbol{C}_{1} boldsymbol{D}_{1} boldsymbol{D}_{2} boldsymbol{C}_{2}, boldsymbol{C}_{2} boldsymbol{D}_{2} boldsymbol{D}_{3} boldsymbol{C}_{3} ldots ) and so on are obtained. Sum of areas of all the trapezium is – A ( cdot frac{r^{2}}{2 sqrt{3}} ) B. ( frac{9 r^{2}}{2 sqrt{3}} ) ( mathrm{c} cdot frac{9 r^{2}}{sqrt{3} r^{2}} ) D. ( frac{r^{2}}{9 sqrt{3}} ) | 8 |

68 | A regular polygon with 4 sides has area: ( mathbf{A} cdot ) length ( times ) breadth B. (side) ( ^{2} ) C. ( frac{sqrt{3}}{4}(text { side })^{2} ) D ( cdot frac{1}{2}(text { sum of two parallel sides }) ) | 8 |

69 | The two adjacent sides of a parallelogram are ( 25 mathrm{cm} ) and ( 40 mathrm{cm} ) respectively. The altitude drawn on the Ionger side is ( 18 mathrm{cm}, ) then the area of the parallelogram is A ( cdot 450 mathrm{cm}^{2} ) B ( .720 mathrm{cm}^{2} ) ( c cdot 500 mathrm{cm}^{2} ) D. none of these | 8 |

70 | A teak wood log is cut first in the form of a cuboid of length ( 2.3 mathrm{m}, ) width ( 0.75 mathrm{m} ) and of a certain thickness. Its volume is ( 1.104 mathrm{m}^{3} . ) How many rectangular planks of size ( 2.3 mathrm{m} times 0.75 mathrm{m} times 0.04 mathrm{m} ) can be cut from the cuboid? | 8 |

71 | Draw parallelogram ABCD with the following data: ( A B=6 mathrm{cm}, A D=5 mathrm{cm} ) and ( angle D A B= ) ( 45^{circ} ) Let ( A C ) and ( D B ) meet in 0 and let ( E ) be the mid-point of Bc. Join OE. then, OE II AB. ( Enter 1 if true or 0 otherwise) | 8 |

72 | The length and breadth of a rectangle are in the ratio ( 3: 2 . ) Total cost of fencing it at ( R s 12.5 . ) Per meter is ( R s 25000, ) find its length and breadth. | 8 |

73 | Each surface area of a cube is ( 100 mathrm{cm}^{2} ) If parallel surface of base cut the cube in two equal parts then total surface area of each equal part. | 8 |

74 | The perimeter of a rhombus is ( 146 mathrm{cm} ) and one of its diagonal is ( 55 mathrm{cm} . ) Find the other diagonal and the area of the rhombus. A. ( 24 mathrm{cm} 660 mathrm{sq} . mathrm{cm} ) B. ( 24 mathrm{cm} 330 ) sq. ( mathrm{cm} ) c. ( 48 mathrm{cm} 660 mathrm{sq} . mathrm{cm} ) D. ( 48 mathrm{cm} 1320 ) sq. ( mathrm{cm} ) | 8 |

75 | The cross-section of a canal is trapezium in shape. The canal is ( 12 m ) wide at the top and ( 8 m ) wide at the bottom. If the area of the cross-section is ( 840 s q . m, ) the depth of the canal is: ( mathbf{A} cdot 8.75 m ) в. ( 42 m ) ( c .63 m ) D. ( 84 m ) | 8 |

76 | A flooring tile has the shape of a parallelogram whose base is ( 24 mathrm{cm} ) and the corresponding height is ( 10 mathrm{cm} . ) How many such tiles are required to cover a floor of area ( 1080 m^{2} ? ) A . 20000 B. 35000 c. 45000 D. 65000 | 8 |

77 | The base of a right prism is a Trapezium whose lengths of two Parallel sides are ( 10 c m ) and ( 6 mathrm{cm} ) and distance between them is ( 5 mathrm{cm} . ) If the height of the prism is ( 8 mathrm{cm}, ) its volume is A ( cdot 320 mathrm{cm}^{3} ) B. ( 300.5 mathrm{cm}^{3} ) ( c cdot 310 c m^{3} ) D. ( 300 mathrm{cm}^{3} ) | 8 |

78 | What will be the height of a cuboid whose volume is ( 275 mathrm{cm}^{3} ) and base area is ( 25 mathrm{cm}^{2} ? ) ( A cdot 10 mathrm{cm} ) B. ( 11 mathrm{cm} ) ( c cdot 9 mathrm{cm} ) D. None of these | 8 |

79 | The area of trapezium shaped field is ( 480 m^{2}, ) the distance between two parallel sides is ( 15 mathrm{cm} ) and one of the parallel sides is 20 m. Find the other parallel side. A. ( 44 m ) в. 42 т ( c .43 m ) D. None of these | 8 |

80 | One diagonal of a parallelogram is ( 40 mathrm{cm} ) and the perpendicular distance of this diagonal from either of the outlying vertices is ( 19 mathrm{cm} . ) The area of the parallelogram (in sq. cm) is 4. ( 700 mathrm{cm}^{2} ) ( 3 cdot 380 c m^{2} ) ( c cdot 760 c m^{2} ) ) ( 1140 mathrm{cm}^{2} ) | 8 |

81 | Two points ( A ) and ( B ) with coordinates (1,1) and (-2,3) respectively are given Find the locus of a point ( boldsymbol{P} ) so that the area of ( triangle boldsymbol{P A B} ) is ( mathbf{9} ) sq.units. A. ( 2 x-3 y-13=0 ) B. ( 2 x+3 y-13=0 ) c. ( 5 x-3 y-13=0 ) D. ( 5 x+3 y-13=0 ) | 8 |

82 | Let ( P(2,-4) ) and ( Q(3,1) ) be two given points. Let ( R(x, y) ) be a point such that ( (x-2)(x-3)+(y-1)(y+4)=0 ) area of ( Delta P Q R ) is ( frac{13}{2}, ) then the number of possible positions of ( boldsymbol{R} ) are ( A cdot 2 ) B. 3 ( c cdot 4 ) ( D ) | 8 |

83 | 54. The perimeter of the triangular base of a right prism is 15 cm and radius of the incircle of the triangular base is 3 cm. If the volume of the prism be 270 cm”, then the height of the prism is (1) 6 cm (2) 7.5 cm (3) 10 cm (4) 12 cm | 8 |

84 | Find the breadth of the rectangle whose length is ( 70 mathrm{cm} ) and perimeter ( 200 mathrm{cm} ) | 8 |

85 | Find the area of the triangle formed by the lines ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{2 h} boldsymbol{x} boldsymbol{y}+boldsymbol{b} boldsymbol{y}^{2} ) and ( boldsymbol{l} boldsymbol{x}+boldsymbol{m} boldsymbol{y}+boldsymbol{n}= ) 0 | 8 |

86 | The area of a rectangle and square are same. If the side of a square is ( 80 m ) and length of rectangular park is ( 200 m ) Find breadth of the rectangle. | 8 |

87 | Find the area tabletop, which is in the shape parallelogram with base ( 4 m ) and height ( 5 m ) Find its area. | 8 |

88 | ( operatorname{Let} boldsymbol{A}_{0} boldsymbol{A}_{1} boldsymbol{A}_{2} boldsymbol{A}_{3} boldsymbol{A}_{4} boldsymbol{A}_{5} ) be a regular hexagon inscribed in a circle of unit radius. Then the product of the length of the line segments ( A_{0} A_{1}, A_{0} A_{2} ) and ( boldsymbol{A}_{0} boldsymbol{A}_{4} ) is A ( cdot frac{3}{4} ) в. ( frac{3}{sqrt{3}} ) ( c .3 ) D. ( frac{3 sqrt{3}}{2} ) | 8 |

89 | A man running round a racecourse notes that the sum of the distances of two flag-posts from him is always ( 10 m ) and the distance between the flag-posts is ( 8 m . ) The area of the path he encloses is A. ( 18 pi ) square metres B. ( 15 pi ) square metress c. ( 12 pi ) square metress D. ( 8 pi ) square metres | 8 |

90 | The adjacent sides of a parallelogram are ( 10 m ) and ( 8 m . ) If the distance between the longer sides is ( 4 m ), find the distance between the shorter sides. | 8 |

91 | A rectangle garden has a length ( 3 frac{1}{5} mathrm{m} ) and breadth ( 2 frac{3}{4} mathrm{m} ) what is its area? | 8 |

92 | The base of a parallelogram is twice its height.lf the area of a parllelogram is 72 sq cm ,find the height. | 8 |

93 | ABCD is a parallelogram ( P ) and ( R ) are two points on AB such that the area of parallelogram ABCD is 8 times the are of ( Delta D P R ) If ( P R=5 c m ) then ( C D ) is equal to ( A cdot 10 mathrm{cm} ) B. ( 5 mathrm{cm} ) ( c .20 mathrm{cm} ) D. ( 12 mathrm{cm} ) | 8 |

94 | The diagonals of a quadrilateral are 16 ( mathrm{cm} ) and ( 13 mathrm{cm} . ) If they intersect each other at right angles; find the area of the quadrilateral. | 8 |

95 | Adjacent sides of a parallelogram are ( 5 c m ) and ( 3.5 mathrm{cm} . ) One of its diagonals is ( 6.5 mathrm{cm} . ) Then what is the area of parallelogram? A. ( 8 sqrt{3} mathrm{cm}^{2} ) В. ( 9 sqrt{3} mathrm{cm}^{2} ) ( mathbf{c} cdot 10 sqrt{3} mathrm{cm}^{2} ) D. ( 12 sqrt{3} mathrm{cm}^{2} ) | 8 |

96 | In the given figure, if area of ( triangle A D E ) is ( 60 mathrm{cm}^{2} ; ) state, giving reason, the area of ( triangle A B E ) A ( cdot 60 mathrm{cm}^{2} ) В. ( 120 mathrm{cm}^{2} ) ( mathbf{c} cdot 160 mathrm{cm}^{2} ) D. ( 210 mathrm{cm}^{2} ) | 8 |

97 | 6. Find the dimensions of a rectangle with perimeter 16 cm, whose long side is 3 times its short side. | 6 |

98 | A brass tray is in the shape of a parallelogram was polished at a total ( operatorname{cost} ) pf ( R s 2250 ) at the rate of Rs 2 per ( 10 mathrm{cm}^{2} ). If the altitude of the | 8 |

99 | In the given figure, if area of ( triangle A D E ) is ( 60 mathrm{cm}^{2} ; ) state, giving reason, the area of ( square A B C F ) ( A cdot 120 mathrm{cm}^{2} ) В. ( 110 mathrm{cm}^{2} ) ( c cdot 100 mathrm{cm}^{2} ) D. ( 150 mathrm{cm}^{2} ) | 8 |

100 | Find the area in square meter of a parallelogram, whose base is ( 140 mathrm{cm} ) and altitude is ( 20 mathrm{cm} ) | 8 |

101 | The area of a rectangular park is 3100 ( m^{2} ) and its breadth is 50 m. The value of 4 times Its perimeter is | 8 |

102 | The perimeter of a parallelogram is 22 cm. If the longer side measures ( 6.5 mathrm{cm} ) what is the measure of the shorter side? A. ( 4.5 mathrm{cm} ) B. ( 5.5 mathrm{cm} ) ( c .6 .5 mathrm{cm} ) D. 4.2 ( mathrm{cm} ) | 8 |

103 | Find the area of a rhombus whose perimeter is ( 80 mathrm{m} ) and one of whose diagonal is ( 24 mathrm{m} ) A. 324 sq. ( mathrm{m} ) B. 384 sq.m c. 184 sq.m D. 326 sq.m | 8 |

104 | In the figure, ABCD is a parallelogram. ( boldsymbol{A} boldsymbol{E} perp boldsymbol{D} boldsymbol{C}, boldsymbol{C} boldsymbol{F} perp boldsymbol{A} boldsymbol{D} . ) If ( boldsymbol{A} boldsymbol{B}=mathbf{1 6} mathrm{cm} ) ( A E=8 mathrm{cm} ) and ( C F=10 mathrm{cm} ) then ( A D ) is equal to ( A cdot 12 c m ) B. ( 15 mathrm{cm} ) c. ( 12.8 mathrm{cm} ) D. ( 15.5 mathrm{cm} ) | 8 |

105 | Fill in the blanks: The volume of a cube ( =—–x ) ( x ) A. side ( times ) length ( times ) width B. side ( times ) height ( times ) side ( c cdot ) side ( x ) side ( x ) side D. side ( times ) length ( times ) breadth | 8 |

106 | Which of the following is the correct match with respect to the given question? ABCD’ is a rhombus such that ( angle A C B=40^{circ} ) then ( angle A D B= ) [ begin{array}{ll} mathbf{7 0}^{o} & text { As } angle A D B=mathbf{1} / mathbf{2}left(mathbf{1 8 0}^{circ}-mathbf{4 0}^{circ}right) \ 45^{circ} & angle C+angle D=90^{circ} end{array} ] 50 [ angle B C D=80^{circ} Rightarrow angle A D C=100^{circ} therefore ] [ angle A D B=(1 / 2) x 100^{circ} ] ( 60^{0} quad ) All sides are equal ( mathbf{A} cdot(a) rightarrow(i) ) B. ( (c) rightarrow(i i i) ) c. ( (d) rightarrow(i i i) ) D. ( (b) rightarrow(i v) ) | 8 |

107 | Find the perimeter of trapezium if The length of sides of trapezium are ( 25,11,15,13 c m ) | 8 |

108 | A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are ( 26 mathrm{cm}, 28 mathrm{cm} ) and ( 30 mathrm{cm}, ) and the parallelogram stands on the base ( 28 mathrm{cm}, ) find the height of the parallelogram. | 8 |

109 | The area (in square units) of a regular hexagon of side of which is 2 units each, is A. 8.2 B. 10.4 c. 12.5 D. 18.7 | 8 |

110 | Given a reactangular ground is ( 90 m ) long and ( 32 m ) broad. In the middle of the ground there is a circular thank of radius 14 metres. Find the cost of turfing the remaining portion at the rate of ( R s .2 .50 ) per square meter. A. ( R s .5660 ) в. ( R s .4295 ) c. ( R s .552 ) D. ( R s .6250 ) | 8 |

111 | OPQR is a square, ( M ) and ( N ) are the middle points of the sides ( P Q ) and ( Q R ) respectively. This question has multiple correct options A. ratio of the areas of quadriateral ( O M N R ) and the square is 5: 8 B. ratio of the areas of the ( Delta M Q N ) and ( Delta O M N ) is 1: 3 C. ratio of the areas of the ( Delta O P M ) and ( Delta O R N ) is 1: 1 D. ratio of the areas of quadriateral ( O M Q N ) and the square is 1: 2 | 8 |

112 | The length of two adjacent sides of a parallelogram are respectively ( 51 mathrm{cm} ) and ( 37 mathrm{cm} . ) One of its diagonals is ( 20 mathrm{cm} . ) Find the area of the parallelogram. | 8 |

113 | In the figure, the center of the circle is ( A ) and ABCDEF is a regular hexagon of side ( 6 mathrm{cm} ) Find : : (i) Area of segment BPF (ii) Area of shaded portion | 8 |

114 | ( A B C D ) is a parallelogram of area 162 sq.cm. ( P ) is a point on ( A B ) such that ( boldsymbol{A P}: boldsymbol{P B}=mathbf{1}: mathbf{2} ) Calculate the ratio ( boldsymbol{P} boldsymbol{A}: boldsymbol{D} boldsymbol{C} ) A . 1: 3 B. 3: 1 ( c .3: 2 ) D. 2: 3 | 8 |

115 | 65. A sphere and a hemisphere have the same radius. Then the ratio of their respective total surface areas is (1) 2:1 (2) 1:2 (3) 4:3 (4) 3:4 | 8 |

116 | The ratio of the ratii of two circular cones of hte same height is 1: 2 and height of each come is ( sqrt{3} ) times the smaller radius then curved surface areas of two cones will be the ratio of A . 2: 5 В. ( 10: 2 sqrt{3} ) c. ( 1: sqrt{7} ) D. 3:2 | 8 |

117 | The two parallel sides of a trapezium are ( 1.5 m ) and ( 2.5 m ) respectively. If the perpendicular distance between them is 6.5 metres, the area of the trapezium is: ( mathbf{A} cdot 10 m^{2} ) В. ( 13 m^{2} ) c. ( 20 m^{2} ) ( mathbf{D} cdot 26 m^{2} ) | 8 |

118 | If a rectangle and a parallelogram are equal in area and have the same base and are situated on the same side then the quotient: is A. Equal to 1 B. Greater than 1 c. Less than 1 D. Indeterminate | 8 |

119 | ( ln ) a ( Delta A B C ) median AD is produced to ( x ) such that ( A D=D X ). Prove that ( A B X C ) is a parallelogram. | 8 |

120 | The side of a square is ( 2 mathrm{cm} ) Semicircles are constructed outside the square on two sides of the square. Then area of the whole figure is ( mathbf{A} cdot(4+pi) mathrm{cm}^{2} ) в. ( (4+4 pi) mathrm{cm}^{2} ) c. ( (4+2 pi) c m^{2} ) D. ( 4 pi c m^{2} ) | 8 |

121 | The perimeter of a trapezium is ( 52 mathrm{cm} ) Its non-parallel sides are ( 10 mathrm{cm} ) each and the distance between two parallel sides is ( 8 mathrm{cm} . ) Find the area of the trapezium. | 8 |

122 | Find the area of the following triangles. | 8 |

123 | Find the area of the triangle for the following (i) base ( =6 mathrm{cm}, ) height ( =8 mathrm{cm} ) | 8 |

124 | The area (in square units) of a regular hexagon, each side of which is 2 units, is ( A cdot 8 ) B. 10.392 (approx.) c. 12.5 D. 18 | 8 |

125 | The shaded shape is made of 5 congruent squares. The side of one square is ( 4 mathrm{cm} ). Find the total area of the shaded shape. | 8 |

126 | One side of a parallelogram is ( 8 mathrm{cm} . ) If the corresponding altitude is ( 6 mathrm{cm}, ) then its area is given by A ( cdot 24 mathrm{cm}^{2} ) B. ( 36 mathrm{cm}^{2} ) c. ( 40 mathrm{cm}^{2} ) D. ( 48 mathrm{cm}^{2} ) | 8 |

127 | In a right triangle having angles of ( 30^{circ} ) and ( 60^{circ}, ) the ( 60^{circ} ) angle is bisected. What is the ratio of the segments into which the angle bisector divides the opposite leg? A . 2: 3 B. 3: ( c cdot 1: 2 ) D. 3: E. 2: 5 | 8 |

128 | Look at the measures shown in the adjacent figure and find the area of ( square P Q R S ) | 8 |

129 | Twenty dots will cover one square inch. If a floor measures 5 feet by 2.5 feet, how many dots does it take to cover the floor? A . 1,800 B. 15,000 c. 36,000 D. 45,000 | 8 |

130 | Find the area of parallelogram in which base is ( 2.5 mathrm{cm}, ) and altitude is ( 1.4 mathrm{cm} ) | 8 |

131 | A circle is inscribed in an equilateral triangle of side ( a . ) What is the area of any square inscribed in the circle? A ( cdot frac{a^{2}}{3} ) в. ( frac{a^{2}}{4} ) c. ( frac{a^{2}}{6} ) D. ( frac{a^{2}}{8} ) | 8 |

132 | A man usually gets from one corner of a square lot to the opposite corner by walking along two of the sides. Approximately what percent of the distance does he save if he walks along the diagonal? A . ( 27 % ) B. ( 29 % ) ( c .31 % ) D. ( 33 % ) E . ( 25 % ) | 8 |

133 | The length and breadth of a room are ( 3 x^{2} y^{3} ) and ( 6 x^{3} y^{2} ) respectively. Find its perimeter and area. | 8 |

134 | The area of a trapezium is ( 300 m^{2} ). The perpendicular distance between the two parallel sides is 15 m. If the difference of the parallel side is ( 16 m, ) find the length of the parallel sides. | 8 |

135 | The given plane figure is to be coloured. What will be the expenditure at the rate of ( boldsymbol{R} boldsymbol{s} 15 ) per ( boldsymbol{m}^{2} ? ) A . ( R s 450 ) B. ( R s 480 ) c. ( R s 570 ) D. Rs780 | 8 |

136 | 56. A rectangular tin sheet is 12 cm long and 5 cm broad. It is rolled along its length to form a cylin- der by making the opposite edges just to touch each other. Then the volume of the cylinder is (3) (4) 100 cm | 8 |

137 | Find the area of the following parallelogram | 8 |

138 | n measuring the sides of a rectangle, one side is increases by ( 30 % ), and the other side is decreased by ( 15 % . ) What is the change in its area as a percentage? | 8 |

139 | Find the area of the shaded region in the figure shown. | 8 |

140 | A door of length ( 2 m ) and breadth 1 m is fitted in a wall. The length of the wall is ( 4.5 m ) and breadth is ( 3.6 . ) Find the cost of white washing the wall, if the rate of white washing the wall is ( R s 20 ) per ( m^{2} ) | 8 |

141 | Calculate the area of the quadrilateral ( A B C D ) in which ( A B=32 c m, A D= ) ( 24 c m, angle A=90^{circ} ) and ( B C=C D= ) ( mathbf{5} 2 c m ) | 8 |

142 | Find the area of a trapezium whose parallel sides are of length ( 10 mathrm{cm} ) and 6 cm respectively and the perpendicular distance between the two parallel sides is ( 4.5 mathrm{cm} .left(text { in } c m^{2}right) ) | 8 |

143 | A cubic meter of copper weighing ( 9000 k g ) is rolled into a square bar ( 9 m ) long. an exact cube is cut off from the bar. How much does it weight? A. ( 333.3 mathrm{kg} ) в. ( 320.5 mathrm{kg} ) ( mathrm{c} .349 .1 mathrm{kg} ) D. ( 312.9 mathrm{kg} ) | 8 |

144 | Draw parallelogram ( A B C D ) with the following measurements and calculate its area ( A B=7 mathrm{cm}, A C=10 mathrm{cm} ) and ( angle mathrm{AOB}= ) ( 100^{circ} ) where ( overline{A C} ) and ( overline{B D} ) intersect at 0 | 8 |

145 | The area of rhombus whose diagonals are ( 16 mathrm{cm}, 24 mathrm{cm} ) | 8 |

146 | A rectangle with length ( =18 mathrm{cm} ) and breadth ( =12 mathrm{cm} ) has same perimeter as that of a regular pentagon. Find the side (in ( c m ) ) of the pentagon | 8 |

147 | Find the area of a parallelogram with a base of 34 meters and a height of 8 meters. A ( cdot 262 m^{2} ) B . 272 ( m^{2} ) c. ( 282 mathrm{m}^{2} ) D. 292 ( m^{2} ) | 8 |

148 | Calculate the area of a parallelogram with a base of ( 12 mathrm{m} ) and height of ( 5 mathrm{m} ) ( mathbf{A} cdot 59 m^{2} ) в. ( 60 m^{2} ) ( mathbf{c} cdot 61 m^{2} ) D. 62 ( m^{2} ) | 8 |

149 | The parallel sides of a trapezium are 20 ( mathrm{m} ) and ( 30 mathrm{m} ) and its non parallel sides are ( 6 mathrm{m} ) and ( 8 mathrm{m} ). Find the area of the trapezium. A ( cdot 96 m^{2} ) в. ( 82 m^{2} ) c. ( 100 mathrm{m}^{2} ) D. ( 120 m^{2} ) | 8 |

150 | If each edge of a cube is tripled, then find how many times will its volume become? | 8 |

151 | The perimeter of a rhombus is ( 46 mathrm{cm} . ) If the height of the rhombus is ( 8 mathrm{cm} ); find its area. | 8 |

152 | Find the ( z- ) score that corresponds to the ( 65^{t h} ) percentille of the standard Normal curve. | 8 |

153 | The parallel sides of a trapezium are ( x ) and y in length. The length of the line segement joining the mid points of the non parallel sides is A. ( frac{x+y}{2} ) в. ( x+y ) c. ( frac{2 x+3 y}{2} ) D. ( frac{x y}{2} ) | 8 |

154 | ABCD is a rhombus whose diagonals AC and BD intersect at a point ( 0 . ) If side ( A B ) ( =10 mathrm{cm} ) and diagonal ( mathrm{BD}=16 mathrm{cm}, ) find the length of diagonal AC. | 8 |

155 | Draw parallelogram ABCD with the following measurements and calculate its area. ( A B=8 mathrm{cm}, A C=10 mathrm{cm} ) and ( angle A B C=100^{circ} ) | 8 |

156 | The area of a parallelogram is ( 240 mathrm{cm}^{2} ) and its height is ( 12 mathrm{cm} . ) The base of the parallelogram is : A . 24 CM B. 20 СМ c. 28 см D. none of these | 8 |

157 | ( A B C D ) is a trapezium with ( A B | C D ) ( A D=B C=5 c m, A B=12 c m ) and ( C D=7 c m, ) find the area of trapezium ABCD. | 8 |

158 | A square and an equilateral triangle have the same perimeter. If the diagonal of the square is ( 12 sqrt{2} mathrm{cm} ), then the area of the triangle is: A ( cdot 24 sqrt{3} mathrm{cm}^{2} ) B ( cdot 24 sqrt{2} mathrm{cm}^{2} ) c. ( 64 sqrt{3} mathrm{cm}^{2} ) D. ( 32 sqrt{3} mathrm{cm}^{2} ) | 8 |

159 | Find the area of ( | g m A B C D ) if the area of shaded region is ( 12 mathrm{cm}^{2} ) | 8 |

160 | The area of a square park is the same as a rectangular park. If the side of the square park is ( 60 mathrm{m} 60 mathrm{m} ), find the breadth (in meter) of the rectangular park. Given: Length of the rectangular park is ( 90 mathrm{m} ) | 8 |

161 | The perimeter of a rhombus is ( 146 mathrm{cm} ) One of its diagonals is 55 cm. Then the length of the other diagonal and the area of the rhombus is A. ( 48 mathrm{cm}, 1320 mathrm{cm}^{2} ) B . ( 45 mathrm{cm}, 660 mathrm{cm}^{2} ) c. ( 27.5 mathrm{cm}, 660 mathrm{cm}^{2} ) D. None of these | 8 |

162 | A cuboid is ( 3 mathrm{cm} ) high, ( 4 mathrm{cm} ) wide and 5 cm long. What is its volume? ( mathbf{A} cdot 60 mathrm{cm}^{3} ) B. ( 50 mathrm{cm}^{3} ) ( mathrm{c} cdot 150 mathrm{cm}^{3} ) D. ( 100 mathrm{cm}^{3} ) | 8 |

163 | Find the area of a rhombus whose side is ( 5 mathrm{cm} ) and whose altitude is ( 4.8 mathrm{cm} ) | 8 |

164 | Find the area of a regular hexagon with side of ( 15 mathrm{m} ) and apothem is ( 20 mathrm{m} ) A ( .910 m^{2} ) B. ( 920 m^{2} ) c. ( 900 m^{2} ) D. ( 901 mathrm{m}^{2} ) | 8 |

165 | If in a triangles ( mathrm{XYZ}, mathrm{P}, mathrm{Q} ) are points on XY, YZ respectively such that ( X P=2 P Y ) ( mathrm{XQ}=2 mathrm{QZ}, ) then the ratio, area of ( Delta boldsymbol{X P Q} ) ( operatorname{area~of} Delta X Y Z, ) is A .4: 9 B. 2:3 ( c cdot 3: 2 ) ( D cdot 9: 4 ) | 8 |

166 | The length of a rectangle is ( left(frac{3}{4}right)^{t h} ) of its breadth. If its perimeter is ( 126 mathrm{m} ), then its area will be A . ( 972 m^{2} ) B. ( 640 m^{2} ) ( c cdot 840 m^{2} ) D. 954 ( m^{2} ) | 8 |

167 | Find the area of the region bounded by the curve ( y^{2}=x ) and the lines ( x= ) ( 4, x=9 ) and the ( x- ) axis in the first quadrant. | 8 |

168 | Rohit’s family is planning to build a concrete basketball court in their backyard. How many square metres will be left in the backyard for grass? A. 60 sq. ( mathrm{cm} ) B. 35 sq. ( mathrm{cm} ) c. 31 sq. ( mathrm{cm} ) D. 24 sq. ( mathrm{cm} ) | 8 |

169 | Find the area of the shaded region in the following figure where ( boldsymbol{P Q R S} ) is a rectangle ( 30 mathrm{cm} ) long and the two circles have the same radii. ( (pi=3.14) ) | 8 |

170 | ABCD is quadrilateral, ( A C=19 mathrm{cm} ). the length of perpendicular from B and D on AC are ( 5 mathrm{cm} 7 mathrm{cm} ) respectively. Then, the area of ABCD in sq. cm is: | 8 |

171 | The cross section of a canal is in the shape of trapezium. The canal is ( 15 m ) wide at the top and ( 9 m ) wide at the bottom. If the area of the cross section is ( 720 m^{2}, ) then the depth of the canal is ( mathbf{A} cdot 58.4 m ) B. ( 58.6 m ) c. ( 58.8 m ) D. ( 60 m ) | 8 |

172 | BD is one of the diagonals of a quadrilateral ABCD.AM and CN are the perpendiculars from ( A ) and ( C ) respectively, on BD. Show that ( boldsymbol{a r}(boldsymbol{q u a d} . boldsymbol{A B C D})=frac{1}{2} boldsymbol{B D} cdot(boldsymbol{A M}+ ) ( boldsymbol{C} boldsymbol{N}) ) | 8 |

173 | In the following figure, if the dimensions of the trapezoid are as shown and the area of the trapezoid is ( 144, ) what is the value of ( x ? ) ( A cdot 2 ) B. 3 ( c cdot 4 ) D. 6 E. 8 | 8 |

174 | Find the area of trapezium ( boldsymbol{A B C D} ) | 8 |

175 | The length of the diagonals of a rhombus are ( 24 mathrm{cm} ) and ( 18 mathrm{cm} ). Find the length of each side of the rhombus | 8 |

176 | Find the area of quadrilateral whose vertices taken in order are ( boldsymbol{A}(-mathbf{3}, mathbf{2}), boldsymbol{B}(mathbf{5}, mathbf{4}), boldsymbol{C}(mathbf{7},-mathbf{6}) ) and ( D(-5,-4)(text { in sq. ut }) ) | 8 |

177 | ( A B C D ) is a trapezium in which ( A B | ) ( C D ; B C ) and ( A D ) are non-parallel sides. It is given that ( A B=75 c m, B C= ) ( 42 c m, C D=30 c m ) and ( A D=39 c m ) Find the area of the trapezium. | 8 |

178 | Which of the following statements are true (T) and which are false (F)? In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. | 8 |

179 | Calculate the area of a trapezium whose length of the parallel sides are 30 ( mathrm{cm} ) and ( 20 mathrm{cm} ) and distance between the parallel lines is ( 15 mathrm{cm} ) | 8 |

180 | Find the area of a square, the length of whose diagonal is ( 25 mathrm{cm} ) | 8 |

181 | A rectangular plot is 125 m long and ( 72 m ) broad. Find the cost of fencing it at ( R s 27 ) per metre. | 8 |

182 | A field is ( 225 m ) long and ( 175 m ) wide. It has two roads in its centre of uniform width of ( 5 m ), one parallel to its length and the other parallel to its breadth. Find the cost of levelling the roads at Rs.3 per square metre. A ( . ) Rs. 1975 в. ( R s .1125 ) c. ( R s .592 ) D. Rs.6125 | 8 |

183 | The length and breadth of a rectangle (in ( mathrm{cm} ) ) are ( mathrm{x} ) and ( mathrm{y} ) respectively ( boldsymbol{x} leq ) ( mathbf{3 0}, boldsymbol{y} leq mathbf{2 0}, boldsymbol{x} geq mathbf{0} ) and ( boldsymbol{y} geq mathbf{0} . ) If ( mathbf{a} ) rectangle has a maximum perimeter, then its area is ( ldots ldots ) | 8 |

184 | A wall is made up of square bricks of unit length. Then its area is A. 1 sq unit B. 3 sq units c. 20 sq units D. 24 sq units | 8 |

185 | Calculate the area of a trapezoid with bases of 22 and ( 10 mathrm{m}, ) and a height of 15 ( mathrm{m} ) A ( .240 m^{2} ) В. ( 230 m^{2} ) c. ( 220 m^{2} ) D. ( 210 m^{2} ) | 8 |

186 | Find the area of the following parallelogram | 8 |

187 | Find the area of rhombus if the base is ( 20 c m ) and height is ( 45 c m ) | 8 |

188 | A string of length 12 is bent first into a square PQRS and then into an isosceles triangle PQT by keeping the side PQ of the square as base then area of the Square PQRS: area of the triangle PQT= ( ? ) | 8 |

189 | Given ( boldsymbol{A}(mathbf{0}, mathbf{0}) ) and ( boldsymbol{B}(boldsymbol{x}, boldsymbol{y}) ) with ( boldsymbol{x} in ) (0,1) and ( y>0 . ) Let the slope of the line ( A B ) equal to ( m_{1} . ) Point ( C ) lies on the line ( x=1 ) such that the slope of ( B C ) equal to ( m_{2} ) where ( 0<m_{2}<m_{1} . ) If the area of the ( triangle A B C ) can be expressed as ( left(m_{1}-right. ) ( left.m_{2}right) f(x), ) then the largest possible value of ( boldsymbol{f}(boldsymbol{x}) ) is A. в. ( frac{1}{2} ) c. ( frac{1}{4} ) D. ( frac{1}{8} ) | 8 |

190 | The area of quadrilateral constructed by lines ( |boldsymbol{x}|+|boldsymbol{y}|=mathbf{1} ) is ( A cdot 4 ) B. 3 ( c cdot 2 ) D. | 8 |

191 | The area of a rhombus, one of whose diagonals measures ( 8 mathrm{cm} ) and the side is ( 5 mathrm{cm}, ) is A ( .25 mathrm{cm}^{2} ) B. ( 24 mathrm{cm}^{2} ) c. ( 24.5 mathrm{cm}^{2} ) D. ( 26 mathrm{cm}^{2} ) | 8 |

192 | 75 persons can sleep in a room ( 25 mathrm{m} ) by ( 9.6 . ) If each person requires ( 16 m^{3} ) of air; find the height of the room. ( A cdot 5 m ) B. 3 m ( c cdot 6 m ) D. ( 7 mathrm{m} ) | 8 |

193 | The area of a rhombus is 2016 sq ( mathrm{cm} ) and its side is ( 65 mathrm{cm} . ) The lengths of the diagonals (in cm) respectively are A . 125,35 B. 126,32 c. 132,26 D. 135,25 | 8 |

194 | Edge of a cube whose volume is ( frac{1}{125} ) cu ( mathrm{m} ) is A ( cdot frac{1}{15} mathrm{m} ) в. ( frac{1}{5} mathrm{m} ) c. ( frac{1}{25} mathrm{m} ) D. 125 ( mathrm{m} ) | 8 |

195 | Radius of circle is ( 7 mathrm{cm} ) Find Perimeter and area of circle | 8 |

196 | The sides of a rhombus ABCD are parallel to the lines, ( x-y+2=0 ) and ( 7 x-y+3=0 . ) If the diagonals of the rhombus intersect at ( boldsymbol{P}(1,2) ) and the vertex A(different from the origin) is on the ( y ) -axis, then the ordinate of ( A ) is? | 8 |

197 | Find sides a cube is ( 17.5 mathrm{cm} ) find volum of cube | 8 |

198 | If the vertices of a triangle are ( (1,2),(4,-6), ) and ( (3,5), ) then its area is ( ^{mathbf{A}} cdot frac{23}{2} s q u n i t ) B ( cdot frac{25}{2} ) squnit c. 12 sq unit D. none of these | 8 |

199 | The ratio between the sides of a room is ( mathbf{5}: mathbf{3} . ) The ( operatorname{cost} ) of white-washing the ceiling of the room at 50 P per square metre is Rs.270 and the cost of papering the walls at 10 P per square metre is Rs. 48. The height of the room is | 8 |

200 | What is the volume of a cube whose surface area is ( 150 m^{2} ? ) A ( cdot 25 m^{3} ) в. ( 100 m^{3} ) c. ( 125 m^{3} ) D. ( 1000 m^{3} ) | 8 |

201 | The length of a side of a square garden ( A B C D ) is ( 70 m . A ) minor segment of ( odot(O, O A) ) is drawn on each of two opposite sides for developing lawn, as shown in the figure. Find the area of the lawn. | 8 |

202 | A rectangular park, whose grass area is 10800 sq. ( mathrm{m} ). and the sides are in the ratio of ( 4: 3 . ) Calculate the wire required to cover outer boundry of the park. | 8 |

203 | Find the area of the trapezium. ( mathbf{A} cdot 144 sqrt{3} mathrm{cm}^{2} ) B. ( 154 sqrt{3} mathrm{cm}^{2} ) ( mathbf{C} cdot 162 sqrt{3} mathrm{cm}^{2} ) D. None of these | 8 |

204 | The side of a rhombus is ( 10 mathrm{cm} ) and one diagonal is ( 16 mathrm{cm} . ) The area of the rhombus is ( mathbf{A} cdot 96 c m^{2} ) B. ( 95 mathrm{cm}^{2} ) ( mathbf{c} cdot 94 c m^{2} ) D. ( 93 c m^{2} ) | 8 |

205 | A field in the form of a parallelogram has an area of ( 432 m^{2} . ) Find the length of its diagonal on which the perpendiculars drawn from two vertices on either side of it are ( 12 m ) long. | 8 |

206 | The diagram, given below shows two paths drawn inside a rectangular field ( 80 mathrm{m} ) long and ( 45 mathrm{m} ) wide. The widths of the two paths are ( 8 mathrm{m} ) and ( 15 mathrm{m} ) as shown. Find the area of the shaded portion | 8 |

207 | In the following figure, ( square A B C D ) is a parallelogram. ( D L perp A B ) and ( A B=13 ) ( mathrm{cm}=A D . ) If the area of parallelogram is ( 156 mathrm{cm}^{2} ). Find ( A L ) ( A cdot 5 mathrm{cm} ) B. ( 6 mathrm{cm} ) ( c cdot 7 mathrm{cm} ) ( 0.8 mathrm{cm} ) | 8 |

208 | In figure, what is the approximate area of triangle NJL? A. 3.5 B. 53.72 c. 57.72 D. 80.53 E . 115.44 | 8 |

209 | The produce of a square field when sold at the rate of Rs. 1.50 per 100 sq. metres fetches Rs. ( 1350 . ) What will be the cost of putting a fence all round the field at the rate of 50 paise per metre? A. Rs. 549 B. Rs. 575 c. Rs. 675 D. Rs. 600 | 8 |

210 | A race of ( 16 k m ) is completed in taking 4 rounds of a square field. Then find the length and area of the field. | 8 |

211 | Find the volume of a cube of side ( 9 mathrm{cm} ) in cubic metres | 8 |

212 | Two sides of a parallelogram in the ratio ( mathbf{5}: mathbf{3} ) if its perimeter is ( mathbf{6 4 c m}, ) find this lengths of its sides. | 8 |

213 | A square and an equilateral triangle have same perimeters. If diagonal of square is ( 12 sqrt{2} c m, ) then side of traingle is | 8 |

214 | A plot of land has a shape of a parallelogram. It is to be covered by mud. Find the cost of speeding mud at the rate of ( R s 100 ) per square meter while the adjacent sides of the plot are ( mathbf{3 9} boldsymbol{m} ) and ( mathbf{2 5} boldsymbol{m} ) and the diagonal is ( mathbf{5 6} boldsymbol{m} ) | 8 |

215 | In a rhombus of side ( 10 mathrm{cm} ), one of the diagonals is ( 12 mathrm{cm} ) long. Find the length of the second diagonal. ( mathbf{A} cdot 15 mathrm{cm} ) B. ( 16 mathrm{cm} ) ( c .17 c m ) D. none of the above | 8 |

216 | A municipal corporation wall on road side has dimensions as shown in figure The wall is to be used for advertisements and it yields an earning of ( R s .400 ) per ( m^{2} ) in a year. Find the total amount of revenue earned in a year. | 8 |

217 | The given figure shows a parallelogram ( A B C D ) with area ( 324 mathrm{cm}^{2} . P ) is a point in ( A B ) such that ( A P: P B=1: 2 ) Find the area of ( triangle boldsymbol{A} boldsymbol{P} boldsymbol{D} ) ( mathbf{A} cdot 34 mathrm{cm}^{2} ) B. ( 44 mathrm{cm}^{2} ) c. ( 24 mathrm{cm}^{2} ) D. ( 54 mathrm{cm}^{2} ) | 8 |

218 | ( operatorname{lf}left|begin{array}{lll}boldsymbol{x}_{1} & boldsymbol{y}_{1} & mathbf{1} \ boldsymbol{x}_{2} & boldsymbol{y}_{2} & mathbf{1} \ boldsymbol{x}_{3} & boldsymbol{y}_{3} & mathbf{1}end{array}right|=left|begin{array}{lll}boldsymbol{a}_{1} & boldsymbol{b}_{1} & mathbf{1} \ boldsymbol{a}_{2} & boldsymbol{b}_{2} & mathbf{1} \ boldsymbol{a}_{3} & boldsymbol{b}_{3} & mathbf{1}end{array}right| ) then the two triangles with vertices ( left(x_{1}, y_{1}right),left(x_{2}, y_{2}right),left(x_{3}, y_{3}right) ) and ( left(a_{1}, b_{1}right),left(a_{2}, b_{2}right),left(a_{3}, b_{3}right) ) are A . equal in area B. similar c. congruent D. none of these | 8 |

219 | The adjacent sides of a parallelogram 21 ( mathrm{cm} ) and ( 28 mathrm{cm} . ) If its one diagonal is 35 ( mathrm{cm} ; ) find the area of the parallelogram. | 8 |

220 | Priya bent a plastic wire to form the given figure. The figure is made up of 4 squares and 4 equilateral triangles. Find the length of wire. A. ( 110 mathrm{cm} ) B. ( 90 mathrm{cm} ) ( c .100 mathrm{cm} ) D. ( 80 mathrm{cm} ) | 8 |

221 | ( P ) is a point in the interior of a parallelogram ( A B C D . ) Show that ( boldsymbol{a r}(triangle boldsymbol{A P D})+boldsymbol{a r}(triangle boldsymbol{P B C})= ) ( boldsymbol{a r}(triangle boldsymbol{A} boldsymbol{P B})+boldsymbol{a r}(triangle boldsymbol{P} boldsymbol{D}) ) | 8 |

222 | The sides of an ( 8 times 8 ) square are cut by certain points into pieces of length and 7,2 and 6,3 and 5 and 4 and 4 as shown in the figure above. The area of the quadrilateral determined by these four points are ( A cdot 28 ) в. 36 ( c cdot 48 ) ( D ) | 8 |

223 | Find the area of the quadrilateral whose vertices ( operatorname{are}(mathbf{6}, mathbf{9}),(mathbf{7}, mathbf{4}),(mathbf{4}, mathbf{2}) ) and ( (mathbf{3}, mathbf{7}) ) | 8 |

224 | A plastic box 1.5 m long, 1.25 m wide and ( 65 mathrm{cm} ) deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine the area of the sheet required for making the box? | 8 |

225 | Calculate the area of the figure given below: which is not drawn to scale. ( mathbf{A} .630 mathrm{sq.cm} ) B. 620 sq. ( mathrm{cm} ) c. 640 sq. ( mathrm{cm} ) D. 600 sq. ( mathrm{cm} ) | 8 |

226 | The given figure shows a rectangle ABC inscribed in a circle as shown alongside. ( f(A B=28 mathrm{cm} text { and } B C=21 mathrm{cm}, ) Find the area of the shaded portion of the given figure A . ( 374.5 mathrm{cm}^{2} ) В. 374.5 ( m^{2} ) c. ( 3.745 mathrm{cm}^{2} ) D. ( 37.45 mathrm{cm}^{2} ) | 8 |

227 | The whole surface of a rectangular block is ( 846 mathrm{cm}^{3} . ) Find the volume, if these dimensions are proportional to ( mathbf{5}: mathbf{4}: mathbf{3} ) | 8 |

228 | If the extremities of the base of an isosceles triangle are the points ( (2 a, 0) ) and ( (0, a), ) and the equation of one of the sides is ( x=2 a ), then the area of the triangle is A. ( 5 a^{2} ) squnits в. ( frac{5 a^{2}}{2} ) sq.units c. ( frac{25 a^{2}}{2} ) sq.units D. None of these | 8 |

229 | In the figure, ( O P Q R ) is rhombus, three of whose vertices lie on the circle with centre ( boldsymbol{O} ) f the area of the rhombus is ( 32 sqrt{3} c m^{2} ) find the radius of the circle. | 8 |

230 | Each side of a rhombus is ( 10 mathrm{cm} ) long and one of its diagonals measures 16 ( mathrm{cm} . ) Find the length of the other diagona and hence find the area of the rhombus. | 8 |

231 | Two adjacent sides of a parallelogram are ( 34 mathrm{cm} ) and ( 20 mathrm{cm} . ) One of its diagonals is ( 42 mathrm{cm} . ) Then the area of the parallelogram is ( mathbf{A} cdot 612 mathrm{sq.cm} ) B. 672 sq.cm c. 784 sq.cm D. 796 sq.cm | 8 |

232 | Tanya wants to fix wooden planks on the floor of a room for her pets. The room is ( 13 m ) long and ( 10 m ) broad. Find the cost of fixing the planks at the rate of ( R s 500 ) per square meter. | 8 |

233 | ( boldsymbol{P} boldsymbol{Q} boldsymbol{R} boldsymbol{C} ) parallelogram, ( boldsymbol{Q} boldsymbol{M} ) is the height form ( Q ) to ( R C ) and ( Q N ) is the height from ( Q ) to ( P S ). If ( R C=12 mathrm{cm} ) and ( boldsymbol{Q} boldsymbol{M}=mathbf{7 . 6 c m} . ) Find (a) the area of the parallegram ( P Q R C ) ( (b) Q N ) if ( P S=8 c m ) | 8 |

234 | Find the height of a cuboid whose base area is ( 180 mathrm{cm}^{2} ) and volume is ( 900 mathrm{cm}^{3} ) ? | 8 |

235 | ( A(1,2,3), B(0,4,1), C(-1,-1,-3) ) are the vertices of ( Delta A B C ) and the bisector of angle A meets BC in D then D point is В. ( left(10, frac{2}{5}, frac{1}{2}right) ) ( ^{mathbf{C}} cdotleft(frac{-7}{10}, frac{5}{10},-frac{18}{10}right) ) D. (3,-5,1) | 8 |

236 | Edge of a cube whose volume is 27 cu. cm. is A ( cdot frac{1}{9} c m ) в. ( frac{1}{3} c m ) ( c cdot 3 mathrm{cm} ) D. ( 9 mathrm{cm} ) | 8 |

237 | If each edge of a cube is doubled, how many times will its volume increase? | 8 |

238 | The shape of the top surface of a table is trapezium. Find its area if its parallel sides are 1 m and ( 1.2 m ) and the perpendicular distance between them is ( 0.8 m ) A ( cdot 0.88 m^{2} ) B ( .0 .8 m^{2} ) ( mathbf{c} cdot 8.8 m^{2} ) D. ( 0.88 mathrm{cm}^{2} ) | 8 |

239 | Find the area of the given parallelogram | 8 |

240 | Given the perimeter of rhombus is 40 ( mathrm{cm} ) and one diagonal is ( 12 mathrm{cm} ). The length of second diagonal is A . ( 19 mathrm{cm} ) B. 18 ( mathrm{cm} ) ( c cdot 17 mathrm{cm} ) D. ( 16 mathrm{cm} ) | 8 |

241 | ( ln ) a rhombus ( boldsymbol{A B C D}, angle boldsymbol{A}=mathbf{6 0}^{circ} ) and ( A B=6 mathrm{cm} . ) Then the diagonal ( B D ) is A ( cdot 2 sqrt{3} c m ) в. 6 ст c. ( 12 mathrm{cm} ) D. ( 10 mathrm{cm} ) | 8 |

242 | A swimming pool is ( 18 mathrm{m} ) long and ( 8 mathrm{m} ) wide. Its deep and shallow ends are ( 2 mathrm{m} ) and ( 1.2 mathrm{m} ) respectively. Find the capacity of the pool, assuming that the bottom of the pool slopes uniformly. A . 230.4 cu. ( mathrm{m} ) B. 420.4 cu. ( mathrm{m} ) c. 340.4 cu. ( mathrm{m} ) D. 190.4 cu. ( m ) | 8 |

243 | If the volume of a cube is ( 512 mathrm{cm}^{3} ), then find the length of an edge of the cube | 8 |

244 | If ( P ) is a point inside the scalene triangle ( A B C ) such that ( Delta A P B ) ( Delta B P C ) and ( Delta C P A ) have the same area, then ( P ) must be: A. In centre of ( Delta A B C ) B. Circum centre of ( Delta A B C ) c. Centroid of ( Delta A B C ) D. Ortho centre of ( Delta A B C ) | 8 |

245 | In the given figure, ( D E | B C ), if ( A D= ) ( 1.5 mathrm{cm}, B D=2 A D ) then ( frac{a r(Delta A D E)}{a r(t r a p e z i u m B C E D)} ) | 8 |

246 | The difference between the radii of the smaller circle and the bigger circle is ( 7 mathrm{cm} ) and the difference between the areas of the two circles is 1078 sq ( mathrm{cm} ) What is the radius of the smaller circle in cm? A . 28 B . 21 c. 17.5 D. 35 | 8 |

247 | The perimeter of rhombus is 52 sq. cm. If one of its diagonal is ( 24 mathrm{cm} ; ) find the length of its other diagonal. | 8 |

248 | If the length of the side of the cube is doubled, then the ratio of the volume of the new cube and the orignal cube is A .1: 2 B . 2: 1 c. 4: 1 D. 8: 1 | 8 |

249 | The floor of a building consists of around 3000 tiles which are rhombus shaped and each of its diagonals are ( 45 c m ) and ( 30 c m ) in length. Find the total ( operatorname{cost} ) of flooring if each tile costs rupees 20 per ( m^{2} ) | 8 |

250 | ( A B C D ) is a parallelogram with side ( A B=10 mathrm{cm} . ) Its diagonals ( A C ) and ( B D ) are of length ( 12 mathrm{cm} ) and ( 16 mathrm{cm} ) respectively. Find the area of a parallelogram ( boldsymbol{A B C D} ) | 8 |

251 | A rectangular plot ( 85 ~ m ) long and ( 60 m ) broad is to be covered with grass leaving ( 5 m ) all around. Find the area to be laid with grass. A. 3750 sq. ( mathrm{m} ) B. 5750 sq. ( mathrm{m} ) c. 4750 sq. ( mathrm{m} ) D. 6750 sq. | 8 |

252 | A hemispherical bowl of internal radius ( 9 mathrm{cm} ) is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter ( 3 mathrm{cm} ) and height ( 4 mathrm{cm} . ) How many containers are necessary to empty the bowl? | 8 |

253 | The measurement of a compass-boxis ( 16 c m times 4 c m times 2 c m, ) find the volume of a compass-box. | 8 |

254 | A square and a rectangular plot of land have same perimeter. If the square is of side ( 40 m ) and rectangle is of length 5 decameter. Then area of rectangle is A ( cdot 1500 m^{2} ) В. ( 1600 m^{2} ) c. ( 200 m^{2} ) D. ( 150 m^{2} ) | 8 |

255 | A regular hexagon is inscribed in a circle. If the area of hexagon is ( 24 sqrt{3} mathrm{cm}^{2}, ) find the area of the circle. (Use ( boldsymbol{pi}=mathbf{3 . 1 4} ) ). | 8 |

256 | A garden is ( 90 mathrm{m} ) long and ( 75 mathrm{m} ) broad. ( mathrm{A} ) path ( 5 mathrm{m} ) wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectares. | 8 |

257 | An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is ( 12 d m^{2} ) then the difference of their areas ( left(text { in } d m^{2}right) ) is : A .2 B. 4 ( c cdot 6 ) D. 18 | 8 |

258 | One side of a parallelogram is ( 8 mathrm{cm} . ) If the corresponding altitude is ( 6 mathrm{cm}, ) then its area is given by A ( .24 mathrm{cm}^{2} ) B. 36 ( c m^{2} ) ( c cdot 40 c m^{2} ) D. ( 48 mathrm{cm}^{2} ) | 8 |

259 | ( A B C D ) is a parallelogram and ( B P C ) is a triangle with ( P ) falling on ( A D . ) If the area of parallelogram ( A B C D=26 mathrm{cm}^{2} ) find the area of triangle ( boldsymbol{B} boldsymbol{P} boldsymbol{C} ) | 8 |

260 | Circule of unit radius is in a rectangle of length and ( 10 pi mathrm{m} ) width ( 2 pi ) metres. The area of the remaining portion except the circle is: A ( cdotleft(frac{39}{2} piright) m^{2} ) В ( cdotleft(frac{77}{4} piright) m^{2} ) ( mathbf{c} cdotleft(frac{35}{2} piright) m^{2} ) D. ( (19 pi) m^{2} ) | 8 |

261 | Find the area of parallelogram whose base is ( 48 mathrm{cm} ) and height is ( 25 mathrm{cm} ) | 8 |

262 | State the whether given statement is true or false Show that area of a rhombus is half the product of the length of its diagonals. | 8 |

263 | 66. In A ABC, O is the centroid and AD, BE, CF are three medians and the area of A AOE = 15 cm2. then area of quadrilateral BDOF is (1) 20 cm (3) 40 cm (2) 30 cm (4) 25 cm2 | 8 |

264 | ABCDEF is a regular hexagon with centre ( 0 . ) If area of triangle 0 AB is ( 9 c m^{2}, ) find the area of the hexagon. | 8 |

265 | Area of a rhombus is ( 850 mathrm{cm}^{2} ) If one of its diagonal is ( 34 mathrm{cm} ). Find the length of the other diagonal. | 8 |

266 | For what value of ( k ) the point ( (k, 2-2 k) ) ( (1-k, 2 k) ) and ( (-4-k, 6-2 k) ) are collinear A ( .1,-1 / 2 ) в. ( 1,1 / 2 ) c. ( -1,1 / 2 ) D. ( -1,-1 / 2 ) | 8 |

267 | If a metallic cuboid weighs ( 16 mathrm{kg} ), how much would a miniature cuboid of metal weigh, if all dimensions are reduced to one-fourth of the original? A. ( 0.25 k g ) B. ( 0.50 k g ) c. ( 0.75 k g ) D. ( 1 k g ) | 8 |

268 | All rhombuses are parallelogram. A. True B. False | 8 |

269 | Volume of a cube whose edge measures ( mathbf{5 . 8} mathrm{cm} ) is : A. 195.12 cu cm B. 195.118 cu cm c. 195.112 cu cm D. 195.21 cu cm | 8 |

270 | If ( A B C D ) is a rectangle, ( E, F ) are the mid-points of ( B C ) and ( A D ) respectively and ( G ) is any point on ( E F, ) then ( triangle G A B ) equals. ( ^{mathbf{A}} cdot frac{1}{2}(square A B C D) ) в. ( frac{1}{3}(square A B C D) ) c ( cdot frac{1}{4}(square A B C D) ) D ( cdot frac{1}{6}(square A B C D) ) | 8 |

271 | The height of a parallelogram is three- eights of its base. If the area of the parallelogram is ( 96 mathrm{cm}^{2} ), find its height and base. | 8 |

272 | If the diagonals of a rhombus are ( 24 mathrm{dm} ) and ( 10 mathrm{dm}, ) then the perimeter of the rhombus will be A. ( 68 mathrm{dm} ) B. 60 dm ( c .52 mathrm{dm} ) D. 50 dm | 8 |

273 | In the given figure, ( A B E D ) is a parallelogram in which ( A B=D E= ) ( 10 c m ) and the area of ( triangle B E C ) is ( 72 c m^{2} ) If ( C E=16 mathrm{cm}, ) find the area of the trapezium ( boldsymbol{A B C D} ) | 8 |

274 | The area of regular hexagon if its side is ( 4 c m ) A ( .24 sqrt{3} ) B. ( 4 sqrt{3} ) ( c cdot 5 sqrt{3} ) D. ( 2 sqrt{3} ) | 8 |

275 | Food Corporation of India stacks of bags containing wheat in the shape of cuboidal blocks in an open field on wooden platform and these blocks are covered with tarpaulin. If there be 10 blocks, each having dimensions ( 10 m times 5 m times 3 m, ) then find the cost of the tarpaulin used to cover these blocks at the rate of RS. 12.5 per ( m^{2} ). Assuming that there is negligible wastage of tarpaulin in folds. | 8 |

276 | Calculate the area bounded by the line ( x+y=10 ) and both the coordinates axes. | 8 |

277 | The length of the diagonal of a square is ( 8 sqrt{2} mathrm{cm} . ) Find the length of its side and hence the find the area of the square. | 8 |

278 | Find the area of the parallelogram whose diagonals are ( vec{a}=hat{i}-2 hat{j}+3 hat{k} ) and ( vec{b}=3 hat{i}-2 hat{j}+hat{k} ) | 8 |

279 | In fig. ( A B C D ) is a field in the form of a quadrilateral whose sides are indicated in the figure. if ( angle D A B=90^{circ}, ) find the area of the field. Answer: ( 306 m^{2} ) State whether answer given is true or not A. True B. False | 8 |

280 | One side of a parallelogram is ( 8 mathrm{cm} ) If the corresponding altitude is ( 6 mathrm{cm} ) then its area is given by A ( .24 mathrm{cm}^{2} ) B. 36 ( c m^{2} ) ( c cdot 40 mathrm{cm}^{2} ) D. ( 48 mathrm{cm}^{2} ) | 8 |

281 | If the perimeter of one of the faces of a cube is ( 40 mathrm{cm} ), then what is its volume? | 8 |

282 | If ( Delta A B C sim Delta D E F, B C=3 c m E F= ) ( 4 c m ) and area of ( Delta A B C=54 c m^{2} ) then find the area of ( Delta D E F ? ) | 8 |

283 | ( fleft(1, frac{pi}{6}right),left(2, frac{pi}{3}right) ) and ( left(3, frac{pi}{2}right) ) be the angular points of a triangle.Then the area of the triangle is ( left(frac{13-3 sqrt{3}}{4}right) ) sq.unit ( ^{mathbf{B}} cdotleft(frac{11-3 sqrt{3}}{4}right) ) sq.unit ( ^{c} cdotleft(frac{10-3 sqrt{3}}{4}right) ) sq.unit ( D ) | 8 |

284 | Find the area of the semicircle with diameter ( 6 mathrm{cm} ) A . ( 3.5 pi ) sq.units в. ( 4.5 pi ) sq.units ( mathrm{c} .5 .5 pi ) sq.units D. ( 6.5 pi ) sq.units | 8 |

285 | The number of envelopes that can be made out of sheet of paper ( 384 mathrm{cm} ) by ( 172 mathrm{cm} ) if each envelope requires a piece of paper of size ( 16 mathrm{cm} ) by ( 12 mathrm{cm} ), is A. 340 B. 344 c. 338 D. 342 | 8 |

286 | ABCD is a parallelogram, E and F are the mid-points of ( A B ) and ( C D ) respectively. ( mathrm{GH} ) is any line intersecting ( mathrm{AD}, mathrm{EF} ) and BC at G,P and H respectively. Prove that ( boldsymbol{G} boldsymbol{P}=boldsymbol{P} boldsymbol{H} ) | 8 |

287 | 67. A right pyramid 6 m height has a square base of which the diag- onal is V1152 m. Volume of the pyramid is (1) 144 m3 (2) 288 m3 (3) 576 m3 (4) 1152 m3 | 8 |

288 | If the sum of the diagonals of a rhombus is ( 12 mathrm{cm} ) and its perimeter is ( 8 sqrt{5} mathrm{cm} ) then the lengths of the diagonals are: ( mathbf{A} cdot 6 mathrm{cm} ) and ( 6 mathrm{cm} ) B. ( 7 mathrm{cm} ) and ( 5 mathrm{cm} ) c. ( 8 mathrm{cm} ) and ( 14 mathrm{cm} ) D. ( 9 mathrm{cm} ) and ( 3 mathrm{cm} ) | 8 |

289 | Find the area of trapezium ( boldsymbol{A B C D} ) where ( A B ) is parallel to ( D C . A B= ) ( mathbf{7} mathbf{7} boldsymbol{c m}, boldsymbol{B} boldsymbol{C}=mathbf{2} boldsymbol{8} boldsymbol{c m}, boldsymbol{C} boldsymbol{D}= ) ( 60 c m, D A=26 c m ) | 8 |

290 | 56. The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2. Taking – 22 i = , the height of the moun- tain is : (1) 2.2 km (3) 3 km (2) 2.4 km (4) 3.11 km | 8 |

291 | Find the breadth of a rectangular plot of land, if its area is ( $ $ 440 backslash mathrm{m}^{wedge} 2 $ $ 2 ) and the length is ( 22 m . ) Also find its perimeter (in metre) | 8 |

292 | 56. Each interior angle of a regu- lar polygon is 144º. The num- ber of sides of the polygon is (1) 8 . (2) 9 (3) 10 (4) 11 | 8 |

293 | The area of parallelogram with diagonals ( 6 mathrm{cm}, 10 mathrm{cm} ) is | 8 |

294 | Of the following statements, the one that is incorrect is: A. Doubling the length of a given rectangle doubles the area. B. Doubling the altitude of a triangle doubles the area. C. Doubling the radius of a given circle doubles the area. D. Doubling the divisor of a fraction and dividing its numerator by 2 changes the quotient. | 8 |

295 | The adjacent sides of a parallelogram are ( 8 m ) and 5 m. The distance between the longer sides is 4 m. What is the distance between the shorter sides? ( mathbf{A} cdot 6.4 m ) B. ( 6 m ) c. ( 8.6 m ) D. None of these | 8 |

296 | Area of a parallelogram is ( 400 mathrm{cm}^{2} ) and its height is ( 16 mathrm{cm} . ) Find its base. | 8 |

297 | ABCDEF is a regular hexagon with centre ( 0 . ) If area of triangle ( mathrm{OAB} ) is ( 9 mathrm{cm}^{2} ) find the area of the circle in which the hexagon is inscribed. | 8 |

298 | Find the area of a parallelogram, whose one side is ( 6.8 mathrm{cm} ) and the perpendicular distance of their from the opposite vertex is ( 7.5 mathrm{cm} ) | 8 |

299 | Find the area of the Parallelogram ABCD and hence find the value of ( x ) | 8 |

300 | ( L_{1} ) and ( L_{2} ) are 2 tangent ( y^{2}=16 x ) which markes angle ( tan ^{-1} frac{1}{3} ) with the tangent ( T^{prime} ) to the same parabola at the end point of latus rectum which the ordinate then find the area of ( triangle ) formed ( boldsymbol{L}_{1}, boldsymbol{L}_{2} ? ) | 8 |

301 | mrs Razdan wants to use tiles of length ( 20 mathrm{cm} ) and breadth ( 10 mathrm{cm} ) to cover the floor of hger balcony shown in the figure.What is the area of the balcony? How many tiles does she neeed to buy ( (1 s q m=10,000 s q c m) ? ) | 8 |

302 | If the number of diagonals in a polygon is 44 then find its number of sides. | 8 |

303 | The total surface area of cube is ( 100 mathrm{cm}^{3} . ) Find its volume. ( ^{mathbf{A}} cdotleft(frac{100}{6}right)^{frac{2}{3}} ) ( ^{mathrm{B}}left(frac{100}{6}right)^{frac{1}{2}} ) ( ^{mathrm{C}}left(frac{100}{6}right)^{frac{3}{2}} ) D. None | 8 |

304 | If the area of a triangle is 81 square ( mathrm{cm} ) and its perimeters is ( 27 mathrm{cm} ), them its in radius is A. ( 6 mathrm{cm} ) B. 3 ( mathrm{cm} ) c. ( 1.5 mathrm{cm} ) D. none of these | 8 |

305 | Four equal circles each of radius ( a ) units touch one another. the area enclosed between them in square units, is ( left(operatorname{take} pi=frac{22}{7}right) ) ( A cdot 3 a^{2} ) B. ( frac{6 a^{2}}{7} ) c. ( frac{41 a^{2}}{7} ) D. ( frac{a^{2}}{7} ) | 8 |

306 | Two adjacent sides of a parallelogram are ( 10 mathrm{cm} ) and ( 12 mathrm{cm} . ) If one diagonal of it is ( 16 mathrm{cm} ) long; find area of the parallelogram. Also, find distance between its shorter sides. A ( cdot 119.8 mathrm{cm}^{2} ; 11.42 mathrm{cm} ) В. ( 136.74 mathrm{cm}^{2} ; 19.58 mathrm{cm} ) c. ( 127 mathrm{cm} ; 5.85 mathrm{cm} ) D. None of these | 8 |

307 | From a circular card sheet of radius 14 ( mathrm{cm}, ) two circles of radius ( 3.5 mathrm{cm} ) and ( mathrm{a} ) rectangle of length ( 3 mathrm{cm} ) and breadth 1 ( mathrm{cm} ) are removed.(as shown in the adjoining figure). Find the area of the emaining sheet. ( left(text { Take } pi=frac{22}{7}right) ) | 8 |

308 | In the figure ( 1, ) find the area of the parallelogram | 8 |

309 | The area of a rhombus is ( 48 mathrm{cm}^{2} ). and its perimeter is ( 20 mathrm{cm} . ) What is its length? | 8 |

310 | The sides of a triangle are given as ( a, 2 a+3 ) and ( 3 a-3 . ) If the perimeter is ( 60 c m, ) find the number smaller side of the triangle. | 8 |

311 | The shaded part in the given figure is covered with cement. If its costs Rs. 84 to cement an area of ( 3 mathrm{cm}^{2} ), find the total cost of cementing. A. Rs. 8820 B. Rs. 8125 c. Rs. 8610 D. Rs. 8804 | 8 |

312 | Find the area of the triangle below A . 20 в. 30 ( c .35 ) D. 40 | 8 |

313 | ( A B C D ) is a parallelogram whose diagonals intersects each other at right angles if the length of the diagonals are 16 centimetre and 12 centimetre find the length of all sides and its perimeter | 8 |

314 | In the given figure, if ( A B C D ) is a parallelogram and ( E ) is the mid-point of ( B C, ) then area ( (triangle D E C)=k ) area ( (A B C D) . ) Find ( k ) | 8 |

315 | Two adjacent sides of a parallelogram are ( 10 mathrm{cm} ) and ( 12 mathrm{cm} . ) If one diagonal of it is ( 16 mathrm{cm} ) long; find area of the parallelogram. Also, find distance between its shorter sides. A ( cdot 119.8 mathrm{cm}^{2} ; 11.98 mathrm{cm} ) B . ( 119.9 mathrm{cm}^{2} ; 11.20 mathrm{cm} ) ( mathrm{c} cdot 117.6 mathrm{cm}^{2} ; 10.28 mathrm{cm} ) D. ( 120.8 mathrm{cm}^{2} ; 15.98 mathrm{cm} ) | 8 |

316 | In parallelogram ( A B C D, A B=10 mathrm{cm}, A D= ) ( 24 mathrm{cm} ) and ( mathrm{BD}=26 mathrm{cm}, ) find the area of parallelogram(in ( mathrm{cm}^{2} ) ) | 8 |

317 | External dimensions of a wooden cuboid are ( 30 mathrm{cm} times 25 mathrm{cm} times 20 mathrm{cm} . ) If the thickness of wood is ( 2 mathrm{cm} ) all round find the volume of the wood contained in cuboid formed. | 8 |

318 | If the perimeter of the square carpet is ( 100 m, ) find the area covered by the carpet. | 8 |

319 | The area of a trapezium is ( 138 m^{2} ). The distance and the difference between the lengths of the parallel sides are ( 12 m ) and 7 m respectively. Find the lengths of the parallel sides. | 8 |

320 | Find the area of the following parallelogram | 8 |

321 | A square lawn is surrounded by a path ( 2.5 m ) wide. If the are of path is ( 165 m^{2} ) find the area of the lawn | 8 |

322 | The diagram, given below, shows two paths drawn inside a rectangular field ( 80 mathrm{m} ) long and ( 45 mathrm{m} ) wide. The widths of the two paths are ( 8 mathrm{m} ) and ( 15 mathrm{m} ) as shown. Find the area of the shaded portion | 8 |

323 | A square ( A B C D ) and a circle are drawn a graph sheet such that the vertices of the square ( A B C D ) are ( boldsymbol{A}(-mathbf{2}, mathbf{2}), boldsymbol{B}(mathbf{2}, mathbf{2}), boldsymbol{C}(mathbf{2},-mathbf{2}), boldsymbol{D}(-mathbf{2},- ) and the circle with centre (0,0) and radius ( 2 mathrm{cm} ) is cut off from the above square ( A B C D . ) Find the area of the remaining region in the square ( A B C D ). | 8 |

324 | Find the locus of a point whose co- ordinates are given by ( boldsymbol{x}=boldsymbol{a} boldsymbol{t}^{2}, boldsymbol{y}=boldsymbol{2} boldsymbol{a} boldsymbol{t} ) Where ‘t’ is a parameter | 8 |

325 | The hour hand and the minute hands of a clock are ( 4 mathrm{cm} ) and ( 6 mathrm{cm} ) long respectively Find the sum of distances travelled by their tips in 2 days? | 8 |

326 | The formula for volume of cube is A ( cdot l^{3} ) B. ( 6 l^{2} ) c. ( 4 l^{3} ) D. ( 6 l^{3} ) | 8 |

327 | Find the area of the shaded region | 8 |

328 | Calculate the area of the adjoining figure shown | 8 |

329 | In a given figure,ABCD is a trapezium in which the parallel sides ( A B ) and ( C D ) are both perpendicular to BC.If ( boldsymbol{A B}= ) ( mathbf{1 6}, boldsymbol{A D}=mathbf{1 7} ) and ( boldsymbol{C D}=mathbf{8}, ) then ( mathbf{B C} ) is A .15 B. 25 ( c .25 .5 ) 0.39 | 8 |

330 | There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways. Find the ratio of this park using both ways in ( mathrm{m}^{2} ) | 8 |

331 | A wall 5 m long, ( 30 mathrm{cm} ) wide and ( 4 mathrm{cm} ) height is made of bricks, each measuring ( (22 c m times 12.5 c m times ) 12.5cm ( ) . ) If ( frac{1}{12} ) of the total volume of the wall consists of motor, how many bricks are there in the wall? | 8 |

332 | Show that point ( A(7,5), B(2,3) ) and ( mathrm{C}(6,-7) ) are the vertices of a right triangle. Also find its area. | 8 |

333 | The perimeter of a rhombus is ( 40 mathrm{cm} ) and the length of one of its diagonals is 12 cm then the area of the rhombus is ( mathbf{A} cdot 95 mathrm{cm}^{2} ) B. ( 96 mathrm{cm}^{2} ) c. ( 97 mathrm{cm}^{2} ) D. ( 98 mathrm{cm}^{2} ) | 8 |

334 | The adjoining sketch shows a running tract ( 3.5 ~ m ) wide all around which of two straight paths and two semicircular rings. Find the area of the track. | 8 |

335 | OPQR is a square and ( M, N ) are the middle points of the sides ( P Q ) and ( Q R ) respectively, then the ratio of the areas of the square and the ( triangle O M N ) is A . 4: 1 B . 2: 1 c. 8: 3 D. 7: 3 | 8 |

336 | Find the perimeter of a square which has an area of ( 121 mathrm{cm}^{2} ) | 8 |

337 | Find the area ( left(text {in } c m^{2}right) ) of a parallelogram ( boldsymbol{P Q R S}, ) if ( boldsymbol{P R}=mathbf{2 4} boldsymbol{c m} ) and ( Q U=S T=8 c m ) | 8 |

338 | A trapezium PQRSPQRS. Meassuremnt in centimeters are given as shown in the figure. Find the area of the trapezium. | 8 |

339 | Let ( S_{1}, S_{2}, S_{3}, dots ) be squares such that for each ( n geq 1 ; ) the length of a side of ( S_{n} ) equals the length of a diagonal of ( S_{n+1} ) If the length of a side of ( S_{1} ) is ( 10 mathrm{cm} ) then for which of the following values of ( n ) is the area of ( S_{n} ) less than 1 sq.cm? This question has multiple correct options ( A cdot 7 ) B. 8 c. 9 D. 10 | 8 |

340 | In a cuboid,of 3 sides are ( 4 a^{2} b^{2}, 6 a^{2} b^{2} ) and ( 6 a ), then the volume of the cuboid is A ( cdot 144 a^{5} b^{4} ) B. ( 144 a^{3} b^{2} ) c. ( 144 a^{2} b^{3} ) D. ( 12 a^{2} b^{2} ) | 8 |

341 | The perimeter of a rectangle is ( 13 mathrm{cm} ) and its width is ( 2 frac{3}{4} mathrm{cm} . ) Find its length. | 8 |

342 | Find the fourth vertex of the rhombus formed by (-1,-1),(6,1) and (8,8) | 8 |

343 | Find the area of a quadrilateral whose sides are ( A B=3 c m, B C=4 c m ) ( C D=6 c m ) and ( D A=5 mathrm{cm} ) and diagonal ( boldsymbol{A C}=mathbf{5} boldsymbol{c m} ) ( mathbf{A} cdot 16 mathrm{cm}^{2} ) B. ( 18 mathrm{cm}^{2} ) ( c cdot 20 c m^{2} ) D. ( 22 mathrm{cm}^{2} ) | 8 |

344 | A verandah of width ( 2.25 mathrm{m} ) is constructed all along outside a room which is ( 5.5 m ) long and 4 m wide. Find The cost of cementing the floor of the verandah at the rate of ( R s .200 ) per ( m ) | 8 |

345 | The diagonal of a rhombus are ( 15 mathrm{cm} ) and ( 18 mathrm{m} . ) Find its area and side. | 8 |

346 | The area of the pentagon whose vertices ( operatorname{are}(4,1),(3,6),(-5,1),(-3,-3) ) and (-3,0) is A . 30 sq. units B. 60 sq. units c. 120 sq units D. none of these | 8 |

347 | If one side of rhombus has end points (4,5) and (1,1) then the maximum area of the rhombus is: A. 50 sq. units B. 25 sq. units c. 30 sq. units D. 20 sq. units | 8 |

348 | In a swimming pool measuring ( 90 mathrm{m} ) by ( 40 mathrm{m}, 150 ) men take a dip. If the average displacement of water by a man is ( 8 m^{3} ) what will be the rise in water level? A. ( 33.33 mathrm{cm} ) B. ( 30 mathrm{cm} ) c. ( 20 mathrm{cm} ) D. ( 25 mathrm{cm} ) | 8 |

349 | The areas of three adjacent faces of a cuboid are ( a, b ) and ( c . ) If the volume of the cuboid is ( V ), then what is ( V^{2} ) equal to A ( cdot a b c ) B. ( a b+c ) c. ( a+b+c ) D. None of these | 8 |

350 | Find the area of a parallelogram having base ( 4 mathrm{cm} ) and height ( 2 mathrm{cm} ) A. 6 sq. ( mathrm{cm} ) B. 8 sq. ( mathrm{cm} ) c. 10 sq. ( mathrm{cm} ) D. 12 sq. ( mathrm{cm} ) | 8 |

351 | If the diagonals of a parallelogram are equal, it is a A. rectangle B. square c. trapezium D. none of these | 8 |

352 | The area of a trapezium is ( 105 mathrm{cm}^{2} . ) If one of the parallel sides is ( 28 mathrm{cm} ) and the distance the parallel sides is ( 5 mathrm{cm} ) find the length of the other parallel side. | 8 |

353 | The figure shows Ghanshyam’s squareshaped field. Find the perimeters of the cabbage and cauliflower patches. Are they equal? | 8 |

354 | The length of a rectangular garden is 2 feet longer than 3 times its width. If the perimeter of the garden is 100 feet, find the width of the garden. A . 12 B. 20 c. 40 ( D ) | 8 |

355 | The following figures ( G U N S ) Find ( x text { and } y text { .(Lengths are in } c m) ) | 8 |

356 | Find the area of a rhombus whose diagonals are ( 12 mathrm{cm} ) and ( 13 mathrm{cm} ) | 8 |

357 | Perimeter of the figure is ( mathbf{A} cdot 68.2 mathrm{cm} ) ( mathbf{B} cdot 68.1 mathrm{cm} ) ( mathrm{C} cdot 86.3 mathrm{cm} ) D. ( 68.3 mathrm{cm} ) | 8 |

358 | The dimensions of a rectangle ABCD are ( 51 mathrm{cm} 25 mathrm{cm} . ) A trapezium ( P Q C D ) with its parallel sides ( mathrm{QC} ) and ( mathrm{PD} ) in the ratio ( 9: 8, ) is cut off from the rectangle as shown in the figure. If the area of the trapezium PQCD is ( frac{5}{6} ) th part of the area of the rectangle, find the length ( Q C ) | 8 |

359 | DL and BM are the height on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is ( 1470 mathrm{cm}^{2}, mathrm{AB}=35 ) and ( mathrm{AD}=49 mathrm{cm} ) find the length of BM and DL. | 8 |

360 | A picture frame has dimensions ( 24 mathrm{cm} times 28 mathrm{cm} . ) Find the area of the picture | 8 |

361 | A swimming pool is ( 100 mathrm{m} ) long and ( 15 mathrm{m} ) wide its deep and ( 24 mathrm{m} ) height respectively. Find the capacity of the pool A. ( 36,000 mathrm{m} ) в. ( 36,000 m^{3} ) c. ( 36,000 m^{2} ) D. 36,000 ( c m ) | 8 |

362 | ( P ) is a point in the interior of ( a ) parallelogram ( A B C D . ) Show that ( boldsymbol{a r}(triangle boldsymbol{A P B})+boldsymbol{a r}(triangle boldsymbol{P C D})= ) ( frac{1}{2} a r(A B C D) ) | 8 |

363 | PQRS is a parallelogram. QM is the height from ( Q ) to ( S R ) and ( Q N ) is the height from ( Q ) to PS. If ( S R=12 c m ) and ( Q M=7.6 ) ( mathrm{cm} . ) Find the area of the parallelogram PQRS. | 8 |

364 | If the side of a rectangle are ( 7 mathrm{cm} ) and ( 5 mathrm{cm}, ) find its area. | 8 |

365 | The circumference of a circle is ( 22 mathrm{cm} ) Then the area is | 8 |

366 | Two sides of the parallelogram PQRS are ( 6 mathrm{cm} ) and ( 4 mathrm{cm} . ) The height corresponding to the base RS is ( 3 mathrm{cm} ) Find Area of parallelogram. | 8 |

367 | If the perimeter of an isosceles triangle is ( 11 mathrm{cm} ) and its base is ( 5 mathrm{cm}, ) its area is ( frac{5}{4} sqrt{11} mathrm{cm}^{2} . ) State true of false and give reason | 8 |

368 | The height of a parallelogram of area ( 350 c m^{2} ) and base ( 25 mathrm{cm} ) is ( A cdot 12 mathrm{cm} ) B. ( 13 mathrm{cm} ) c. ( 14 mathrm{cm} ) D. ( 15 mathrm{cm} ) | 8 |

369 | Find the perimeter of each of the following closed figures: (ii) | 8 |

370 | If a copper wire is bend to make a square whose area is ( 324 mathrm{cm} 2 ). If the same wire is bent to form a semicircle, then find the radius of semicircle. | 8 |

371 | In the given figure ( A B C D E, E Y= ) ( boldsymbol{C Y}=boldsymbol{4} boldsymbol{c m}, boldsymbol{A} boldsymbol{X}=boldsymbol{B} boldsymbol{X}= ) ( 6 c m, D E=D C=5 c m, D X=9 mathrm{cm} ) ( D X ) is perpendicular to ( E C ) and ( A B ) Find the area of ( A B C D E ) | 8 |

372 | A brass tray in the shape of a parallelogram was polished at a total ( operatorname{cost} ) of ( operatorname{Rs} 2,250 ) at the rate of Rs 20 per ( 10 mathrm{cm}^{2} . ) If the altitude of the parallelogram is ( 45 mathrm{cm}, ) find the length of its base. | 8 |

373 | Find the area of square with Perimeter ( mathbf{1 0 0 c m} ) | 8 |

374 | Find the area of a quadrilateral one of whose diagonals is ( 30 mathrm{cm} ) long and the perpendiculars from the two other vertices on this diagonal are ( 19 mathrm{cm} ) and ( 11 mathrm{cm} ) respectively. A ( cdot 450 mathrm{cm}^{2} ) В. ( 540 mathrm{cm}^{2} ) D. ( 350 mathrm{cm}^{2} ) | 8 |

375 | If ( D ) and ( E ) are the mi-points of the sides ( A B ) and ( A C, ) respectively of the ( triangle A B C ) what percent of the whole triangular region is the area of the trapezium ( boldsymbol{B C E D} ) ? A . ( 50 % ) B . 25% c. ( 75 % ) D. 60% | 8 |

376 | If the area of a rectangle is equal to the area of a square and length of the rectangle is equal to the perimeter of the square, then the breadth of rectangle is A. side ( div 2 ) B. ( (text {side})^{2} div 2 ) ( c cdot operatorname{side} div 4 ) D. side ( div 3 ) | 8 |

377 | The length of a rectangle with area ( 35 c m^{2} ) is ( 7 c m ) What is its breadth. | 8 |

378 | The perimeter of the incircle is ( 30 mathrm{m} ) and its radius ( 10 mathrm{m} . ) What is the area of the triangle? A. 150 sq. ( mathrm{m} ) В. 140 sq. ( mathrm{m} ) c. 130 sq. ( mathrm{m} ) D. 120 sq. ( m ) | 8 |

379 | Draw parallelogram ABCD with the following measurements and calculate its area. ( A C=8 c m, B D=6 c m ) and ( angle C O D= ) ( 90^{circ} ) where ( overline{A C} ) and ( overline{B D} ) intersect at 0 | 8 |

380 | The area of a rhombus is ( 90 mathrm{cm}^{2} ). If one of the diagonal is ( 14 mathrm{cm}, ) what is the length of the other diagonal? | 8 |

381 | The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden. [Length of the rectangle is ( 20-(3.5+ ) 3.5 ) metres ( ] ) A ( cdot 129.5 mathrm{m}^{2} ; 48 mathrm{m} ) B . ( 179.5 mathrm{m}^{2} ; 48 mathrm{m} ) c. ( 129.5 mathrm{cm}^{2} ; 48 mathrm{m} ) D. ( 129.5 mathrm{m}^{2} ; 88 mathrm{cm} ) | 8 |

382 | ( D L ) and ( B M ) are the height on sides ( A B ) and ( A D ) respectively of parallelogram ( A B C D ) figure. If the area of the parallelogram is ( 1470 mathrm{cm}^{2} ) ( A B=35 mathrm{cm} ) and ( A D=49 mathrm{cm}, ) find the ength of ( B M ) and ( D L ) | 8 |

383 | 70. The parallel sides of a trapezi- um are in a ratio 2:3 and their shortest distance is 12 cm. If the area of the trapezium is 480 sq. cm., the longer of the par- allel sides is of length: (1) 56 cm (2) 36 cm (3) 42 cm (4) 48 cm | 8 |

384 | In the figure ( C ) is a right angle DE ( wedge A B ) ( A E=6, E B=7 ) and ( B C=5 . ) The area of the quadrilateral EBCD is A. 27.5 B . 25 c. 22.5 D. 20 | 8 |

385 | Curved surface area of a hollow cylinder is ( 4224 mathrm{cm}^{2} . ) A rectangular sheet having width ( 33 mathrm{cm} ) is formed cutting it along its height. Find perimeter of sheet. | 8 |

386 | Find the area of the triangle formed by the line ( 3 x+4 y=12 ) and the ( c o ) ordinate axes. | 8 |

387 | Perimeter of a rectangular garden is ( 1.2 times 10^{5} k m ) and length is ( 0.2 times ) ( 10^{5} k m . ) Find the area of the garden in standard form. ( mathbf{A} cdot 8 times 10^{6} k m^{2} ) B . ( 0.8 times 10^{8} k m^{2} ) c. ( 80 times 10^{8} k m^{2} ) D. ( 8.0 times 10^{8} k m^{2} ) | 8 |

388 | In a square garden of ( 3.5 mathrm{m}, ) four flower beds were laid out as shown. The remaining area of the garden is ( 7.25 m^{2} ) If all flower beds are of same size find length of each if the breadth of each flower bed is ( 50 mathrm{cm} ) | 8 |

389 | The area of a rhombus is ( 84 mathrm{m}^{2} ) and its length of one diagonal is 24 m. Find the side of the rhombus | 8 |

390 | The lengths of the shorter and longer parallel sides of a trapezium are ( boldsymbol{x} ) cm and ( y ) cm respectively. If the area of the trapezium is ( left(x^{2}-y^{2}right), ) then the height of the trapezium is: A . ( x ) в. ( (x+y) ) c. ( y ) D. ( 2(x-y) ) | 8 |

391 | Show that the four lines ( a x pm b y pm c= ) 0 enclose a rhombus whose area is ( frac{2 c^{2}}{a b} ) | 8 |

392 | How many person can be accommodated in hall of length ( 16 mathrm{m} ) breadth ( 12.5 mathrm{m} ) and height 4.5 assuming that ( 3.6 m^{3} ) of air is required for each person? | 8 |

393 | Find the area of a square, if the measure of its each diagonal is ( 12 mathrm{cm} ) | 8 |

394 | The area of a parallelogram is ( y c m^{2} ) and its height is ( h ) cm. The base of another parallelogram is ( x ) cm more than the base of the first parallelogram and its area is twice the area of the first. Find, in terms of ( y, h ) and ( x, ) the expression for the height of the second parallelogram. A ( cdot frac{2 h y}{y+x h} c m ) B. ( frac{2 h y}{x+x h} ) cm c. ( frac{2 y}{y+x h} c m ) D. None of these | 8 |

395 | The figure above shows a parallelogram ( A B C D ) with ( A C=3 ) and ( A D=5 ) Calculate the area of parallelogram ( A B C D ) A . 12 B. 15 c. 18 D. 2 | 8 |

396 | A triangle and a parallelogram have the same base and some area. If the sides of the triangle are ( 26 mathrm{cm}, 28 mathrm{cm} ) and 30 ( mathrm{cm} ) and the parallelogram stands on the base ( 28 mathrm{cm} . ) Find the height of the parallelogram. | 8 |

397 | If the edges of cube are halved, then its volume become is A. 4 times B. 8 times c. ( frac{1}{8} ) times D. ( frac{1}{2} ) times | 8 |

398 | A box measuring ( 51 c m times 36 c m times ) 18cm. In this box, how many compass- boxes measuring ( 17 mathrm{cm} ) in length, ( 9 mathrm{cm} ) in width and ( 2 mathrm{cm} ) in height can be arranged? | 8 |

399 | The length of each side of a square field is ( 63 mathrm{m} ). What is the area of the field? | 8 |

400 | The diagonals of parallelogram are 48 and ( 30 c m ) find its area | 8 |

401 | ABCD is a trapezium in which ( boldsymbol{A B} | ) ( C D, ) if ( A B=7 mathrm{cm}, D C=3 mathrm{cm} ) and if the area of the trapezium is ( 18 mathrm{cm}^{2} ), then the area of ( triangle B C D ) is A ( cdot 5 frac{2}{5} c m^{2} ) в. ( 6 frac{2}{5} mathrm{cm}^{2} ) c. ( 7 frac{2}{5} c m^{2} ) D. ( 8 frac{2}{5} c m^{2} ) | 8 |

402 | The ratio of two adjacent sides of a parallelogram is 3: 4 Its perimeter is ( 105 mathrm{cm} ) Find its area if altitude corresponding to the larger is ( 15 mathrm{cm} ) в. ( 600 mathrm{cm}^{2} ) ( c cdot 300 c m^{2} ) D. ( 450 mathrm{cm}^{2} ) | 8 |

403 | Find the area of the quadrilateral ABCD whose vertices are ( A(-3,-1), B(-2,-4) ) ( C(4,-1) ) and ( D(3,4) ) | 8 |

404 | A lake on the map has an area of ( 0.15 mathrm{cm}^{2} . ) work out the actual area of the lake. | 8 |

405 | In the figure drawn below, its dimensions are given in meters. If ( boldsymbol{C}= ) ( 3, ) find the total cost to fence the garden if the cost of fencing is ( 7 / m^{2} ) | 8 |

406 | What is the area of a regular hexagon with sides of 2.5 in and apothem is 12 in? ( mathbf{A} cdot 89 ) in ( ^{2} ) B. 14.5 in ( ^{2} ) c. 80 in ( ^{2} ) D. 90 in ( ^{2} ) | 8 |

407 | A rectangle and a parallelogram have equal areas. If the sides of the rectangle are ( 10 m ) and ( 12 m ) and the base of the parallelogram is ( 20 m, ) then the altitude of the parallelogram is: A . ( 7 m ) B. ( 6 m ) ( c .5 m ) D. ( 3 m ) | 8 |

408 | A rectangular tank containing water is ( 5 mathrm{m} ) long, ( 3 mathrm{m} ) broad and ( 2 mathrm{m} ) deep. Find how much the water will rise, if a block of lead ( 1 mathrm{m} times 45 mathrm{cm} times 30 mathrm{cm} ) is put in the tank? A. ( 9 mathrm{cm} ) B. ( 90 mathrm{cm} ) ( mathrm{c} .9 mathrm{mm} ) D. 9 m | 8 |

409 | The two adjacent sides of a parallelogram are ( 5 mathrm{cm} ) and ( 4 mathrm{cm} ) respectively and if the respective diagonal is ( 7 mathrm{cm}, ) then find the area of the parallelogram? ( A cdot 8 sqrt{6} ) B. ( 6 sqrt{6} ) c. ( 4 sqrt{6} ) D. ( 8 sqrt{3} ) | 8 |

410 | Find the area of the following trapeziums | 8 |

411 | Find the area of a regular polygon of 7 sides whose each side measures ( 4 mathrm{cm} ) and the circumradius is ( 3 mathrm{cm}(sqrt{5}= ) ( mathbf{2 . 2 3 6}) ) A ( cdot 31.304 mathrm{cm}^{2} ) B. ( 31.804 mathrm{cm}^{2} ) c. ( 31.304 m^{2} ) D. None of these | 8 |

412 | The ratio between the length and breadth of a rectangular garden is 5: 3 If the perimeter of the garden is 160 meters, what will be the area of ( 5 m ) wide road around its outside? A. ( 600 m^{2} ) B. ( 1200 m^{2} ) ( mathrm{c} cdot 900 m^{2} ) D. ( 1000 m^{2} ) | 8 |

413 | If the base of a parallelogram decreases by ( 20 % ), and the height increases by, 40 ( % ) by what percent does the area increase? | 8 |

414 | The cost of paving the floor at the rate of Rs. 18 per ( m^{2} ) A . Rs. 10239 3. Rs 8839 ( c . ) Rs. 7125 D. Rs. 5040 | 8 |

415 | If the base of a parallelogram is ( (x+4) ) altitude to the base is ( (x-3) ) and the area is ( left(x^{2}-4right), ) then what is the actual area equal to? A. 60 sq units B. 45 sq units c. 77 sq units D. 96 sq units | 8 |

416 | The area of a rhombus is ( 72 mathrm{cm}^{2} ) and its perimeter is ( 32 mathrm{cm}, ) altitude is ( A cdot 8 c m ) в. 9 ст ( c .4 mathrm{cm} ) D. None of these | 8 |

417 | Find the area of the pentagonal park shown in figure in two different ways. A ( .600 m^{2} ) B. ( 800 m^{2} ) ( c cdot 60 m^{2} ) D. ( 600 mathrm{cm}^{2} ) | 8 |

418 | Find the area of the following rhombuses | 8 |

419 | Two parallel sides of a trapezium are ( 60 mathrm{cm} ) and ( 77 mathrm{cm} ) and the other two sides are ( 15 mathrm{cm} ) and ( 26 mathrm{cm} ). Find the area of the trapezium. | 8 |

420 | In the given figure, if area of parallelogram ( A B E F ) is ( 96 mathrm{cm}^{2} ; ) state giving reason, the area of ( triangle A D B ) ( mathbf{A} cdot 48 mathrm{cm}^{2} ) B. ( 38 mathrm{cm}^{2} ) ( mathrm{c} cdot 58 mathrm{cm}^{2} ) ( mathrm{D} cdot 68 mathrm{cm}^{2} ) | 8 |

421 | The area of rectangle is ( 540 mathrm{cm} ) and its length is ( 36 mathrm{cm} ). Find its width and perimeter. | 8 |

422 | The parallel sides of a trapezium are ( 15 c m ) and ( 9 c m . ) The distance between them is ( 5 c m ). A rectangle has same area as the trapezium. If its length is ( 10 mathrm{cm} ) what is its breadth? A ( .6 mathrm{cm} ) в. 3 ст ( c .5 mathrm{cm} ) D. ( 10 mathrm{cm} ) | 8 |

423 | The length, breadth and height of a cuboid are in the ratio ( 6: 5: 3 . ) If the total surface area is ( 504 mathrm{cm}^{2} ), find its dimension. Also find the volume of the cuboid. | 8 |

424 | If the perimeter of an isosceles triangle is 36 and the altitude to the base is 6 find the length of the altitude to one of the legs. A . 4.8 B. 6 c. 9.6 D. 10 E. cannot be found on the basis of the given data | 8 |

425 | The length of a rectangle is 10 m more than its breadth. if the perimeter of rectangle is 80 m. find the dimensions and area of the rectangle. | 8 |

426 | A cube of edge ( 3 mathrm{cm} ) of iron weighs ( 12 mathrm{g} ) What is the weight of a similar cube of iron whose edge is ( 12 mathrm{cm} ) A. 768 g в. 678 g c. ( 964 mathrm{g} ) D. ( 864 mathrm{g} ) | 8 |

427 | The perimeter of a triangle is ( 9 m^{2}- ) ( 2 n+8 ) and its two sides are ( 4 m^{2}+3 n ) and ( 7 m^{2}+5 n-12 . ) Find the third side of the triangle. A ( cdot m^{2}-10 n-10 ) B. ( -2 m^{2}-10 n+20 ) c. ( -2 m^{2}-14 n+20 ) D. ( m^{2}-10 n+10 ) | 8 |

428 | A rectangle and a parallelogram are on the same base and between the same parallels. If the area of the rectangle is ( 50 c m^{2}, ) then what is the area of the parallelogram? ( mathbf{A} cdot 20 mathrm{cm}^{2} ) B. ( 60 mathrm{cm}^{2} ) ( mathbf{c} cdot 30 c m^{2} ) D. ( 50 c m^{2} ) | 8 |

429 | The perimeter of a rhombus is ( 40 mathrm{cm} ) and the measure of an angle is ( 60^{circ} ) then the area of it is – B ( cdot 75 sqrt{3} mathrm{cm}^{2} ) D. ( 50 sqrt{3} mathrm{cm}^{2} ) | 8 |

430 | ABCD is a trapezium with ( A B ) and ( C D ) parallel. If ( mathrm{AB}=mathbf{6}, mathrm{BC}=mathbf{5}, mathrm{CD}=mathbf{3}, mathrm{DA}=mathbf{4} ) ( A=90^{circ} ) the area of ( A B C D ) is? A .27 B. 12 c. 18 D. 15 | 8 |

431 | (4) equallid 61. In APGR, the line drawn from the vertex P intersects QR at a point S. If QR = 4.5 cm and SR = 1.5 cm then the ratios of the area of triangle POS and trian- gle PSR is (1) 4:1 (2) 3:1 (3) 3:2 (4) 2:1 | 8 |

432 | A circular disc of area ( A_{1} ) is given with its radius as diameter of a circular disc of area ( A_{2} ) is cut out of it. The area of the remaining disc is denoted by ( A_{3} . ) Then ( mathbf{A} cdot A_{1} A_{3}16 A_{2}^{2} ) ( mathbf{c} cdot A_{1} A_{3}=16 A_{2}^{2} ) D. ( A_{1} A_{3}>2 A_{2}^{2} ) | 8 |

433 | Calculate the area of a regular pentagon with sides of ( 2 mathrm{cm} ) and apothem is 12 ( mathrm{cm} ) ( A cdot 60 mathrm{cm}^{2} ) B. ( 61 mathrm{cm}^{2} ) ( c cdot 62 c m^{2} ) ( mathrm{D} cdot 63 mathrm{cm}^{2} ) | 8 |

434 | 68. A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is Take n = 22 (1) 125 cm2 (3) 550 cm2 (2) 230 cm? (4) 616 cm2 | 8 |

435 | In the given figure, if parallelogram ABCD and rectangle ABEF are of equal area then: A. Perimeter of ABCD=Perimeter of ABEF B. Perimeter of ABCD Perimeter of ABEF D. Perimeter of ( A B C D=frac{1}{2} ) (Perimeter of ABEF) | 8 |

436 | Three cubes of sides ( 3 mathrm{cm}, 4 mathrm{cm}, ) and 5 ( mathrm{cm} ) respectively are melted and recasted into a larger cube What is the side of the cube so formed? A . ( 12 mathrm{cm} ) B. ( 9 mathrm{cm} ) ( c .8 mathrm{cm} ) D. ( 6 mathrm{cm} ) | 8 |

437 | In a trapezium whose parallel sides measure ( 24 mathrm{cm} ) and ( 15 mathrm{cm} ) and the distance between them is ( 10 mathrm{cm} . ) Find the area of trapezium. A ( cdot 215 mathrm{cm}^{2} ) В. ( 205 mathrm{cm}^{2} ) ( c cdot 195 mathrm{cm}^{2} ) D. ( 295 mathrm{cm}^{2} ) | 8 |

438 | Two squares have sides ( x mathrm{cm} ) and ( (x+5) ) cm. The sum of their areas is 697 sq.cm. Express this as an algebraic equation ( operatorname{in} x ) | 8 |

439 | A square and a regular hexagon have the same perimeter. If the area of the square is ( 2.25, ) calculate the area of the hexagon. A. 2.250 B. 2.598 c. 2.838 D. 3.464 E . 3.375 | 8 |

440 | The radius of the circular base of an ear of corn is ( 6.6 mathrm{cm} ) and its length is ( 11.2 mathrm{cm} . ) If on an average 1 sqcm area contains 2 corn kernels, find the total number of kernels on an ear of corn. | 8 |

441 | Find the length of a diagonal of rhombus whose area is ( 100 m^{2} ) and length of other diagonal is ( 10 m^{2} ) A. ( 10 mathrm{m} ) в. 20 ( c cdot 2 m ) D. ( 1 mathrm{m} ) | 8 |

442 | Let ( A B C D ) be a quadrilateral with area 18, with side ( A B ) parallel to the side ( C D ) and ( A B=2 C D . ) Let ( A D ) be perpendicular to ( A B ) and ( C D . ) If a circle is drawn inside the quadrilateral ( A B C D ) touching all the sides, then its radius is: A . 3 B . 2 ( c cdot frac{3}{2} ) ( D ) | 8 |

443 | The area of the trapezium is 34 sq ( mathrm{cm} ) and the length of one of the parallel side is ( 10 mathrm{cm} ) and its height is ( 4 mathrm{cm} ). Find the length of the parallel side. | 8 |

444 | Each interior angle of a regular polygon is double of its exterior angle. Find the number of sides in the polygon. | 8 |

445 | The diagonals of rhombus are ( 8 mathrm{cm} ) and ( 10 mathrm{cm} ) Then the area of the rhombus is ( mathbf{A} cdot 64 mathrm{cm}^{2} ) В. ( 100 mathrm{cm}^{2} ) ( c cdot 80 c m^{2} ) D. ( 40 mathrm{cm}^{2} ) | 8 |

446 | Consider the following parallelograms. ind the values of the unknowns ( x, y, z ) A ( . X=60^{circ}, Y=100^{circ}, Z=20^{circ} ) B . ( X=28^{circ}, Y=112^{circ}, Z=28^{circ} ) c. ( X=65^{circ}, Y=105^{circ}, Z=20^{circ} ) | 8 |

447 | The internal length, breadth and height of a box are ( 30 mathrm{cm}, 24 mathrm{cm} ) and ( 15 mathrm{cm} ) Find the largest number of cubes which can be placed inside this box if the edge of each cube is ( 4 mathrm{cm} ) | 8 |

448 | A square of side ( 16 mathrm{cm} ) is reduced by a scale factor 0.5 Find the area of the image A ( cdot 16 mathrm{cm}^{2} ) В. ( 32 mathrm{cm}^{2} ) ( mathbf{c} cdot 64 c m^{2} ) D. ( 1024 mathrm{cm}^{2} ) | 8 |

449 | The area of a trapezium is ( 540 mathrm{cm}^{2} . ) If the ratio of parallel sides is 7: 5 and the distance between them is ( 18 mathrm{cm} ), find the lengths of parallel sides. | 8 |

450 | Area of a rhombus is ( 256 mathrm{cm}^{2} ). One of the diagonal is twice of the other diagonal. The sum of the diagonals is: ( mathbf{A} cdot 38 mathrm{cm} ) в. ( 48 mathrm{cm} ) c. ( 28 mathrm{cm} ) D. ( 56 mathrm{cm} ) | 8 |

451 | From a square metal sheet of side ( 28 mathrm{cm}, ) a circular sheet is cut off. Find the radius of the largest possible circular sheet that can be cut. Also find the area of the remaining sheet. A ( .14 mathrm{cm}, 148 mathrm{cm}^{2} ) B. ( 14 mathrm{cm}, 168 mathrm{cm}^{2} ) c. ( 12 mathrm{cm}, 168 mathrm{cm}^{2} ) D. ( 14 mathrm{cm}, 164 mathrm{cm}^{2} ) | 8 |

452 | If (7,3),(6,1),(8,2) and ( (P, 4) ) are the vertices of a parallelogram taken in order then the value of ( P ) is : ( A cdot 4 ) B. 6 c. 7 D. | 8 |

453 | ABCD is a parallelogram with sides ( A B=12 mathrm{cm}, B C=10 mathrm{cm} ) and diagonal ( boldsymbol{A C}=mathbf{1 6} mathrm{cm} . ) Find the approximate area of the parallelogram. ( mathbf{A} cdot 119.8 mathrm{cm}^{2} ) B. ( 103.7 mathrm{cm}^{2} ) ( mathrm{c} cdot 15.7 mathrm{cm}^{2} ) D. None of these | 8 |

454 | Find the area of the given parallelogram | 8 |

455 | A farmer divided his aquare – shaped land into three parts, as shown.he gave two parts to mukesh and the third part to naresh. how much land did each get? | 8 |

456 | The area of quadrilateral ABCD given below is 269.2 sq.units f true then enter 1 and if false then enter ( mathbf{0} ) | 8 |

457 | PQRS is a parallelogram. QM is the height from ( Q ) to ( S R ) and ( Q N ) is the height from ( Q ) to PS. If ( S R=12 c m ) and ( Q M=7.6 ) ( mathrm{cm} . ) Find ( mathrm{QN}, ) if ( mathrm{PS}=8 mathrm{cm} ) | 8 |

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