# Mensuration Questions

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 NoQuestionsClass
1Find 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
2A 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
3A 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
4A 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
5A 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
6Two isosceles triangles have equal vertical angles and their areas are in
the ratio 36: 25 Find the ratio of their
corresponding heights.
8
7f 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
8Which 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
9The 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
11The 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
12The 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
13f 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
14The 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
15The 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
16A 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
17Find 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
18If the volume of a cuboid is ( 880 mathrm{cm}^{3} ) and
area of base is ( 88 mathrm{cm}^{2} ). Find the height.
8
19An 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
20A 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
21Two 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
22Area 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
23A 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
24The 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
25Consider 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
26If 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
27The 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
28A 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
29Find the area of the regular hexagon
PQRST in which each side measures
( 17 mathrm{m} ) and its height is ( 33 mathrm{m} )
8
30The 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
31A 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
33Find 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
34Find 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
35A 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
36If 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
37A 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
38Draw 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
40The 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
41The area of circle if the circumference
is ( 20 pi )
8
42n 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
43Students 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
44Four 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
45The 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
46The 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
48A 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
49Prove 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
50The 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
51The 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
52The 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
53The 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
54Find the area of a parallelogram with
base ( 32 mathrm{cm} ) and height ( 16.5 mathrm{cm} )
8
55The 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
56The 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
57The 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
58Find 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
59If one side of a rhombus has end points
(4,5) and (1,1) then find the maximum area of rhombus.
8
60A 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
6115.
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
6254. 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
63Draw 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
64A 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
65Find the edge of the cube whose volume
is ( 216 m^{3} )
8
66Find area of parallelogram whose base
is ( 24 mathrm{cm} ) and height is ( 5 mathrm{cm} )
8
67If ( 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
68A 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
69The 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
70A 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
71Draw 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
72The 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
73Each 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
74The 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
75The 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
76A 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
77The 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
78What 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
79The 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
80One 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
81Two 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
82Let ( 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
8354. 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
84Find the breadth of the rectangle whose length is ( 70 mathrm{cm} ) and perimeter ( 200 mathrm{cm} )8
85Find 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
86The 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
87Find 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
89A 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
90The 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
91A rectangle garden has a length ( 3 frac{1}{5} mathrm{m} ) and breadth ( 2 frac{3}{4} mathrm{m} ) what is its area?8
92The base of a parallelogram is twice its
height.lf the area of a parllelogram is 72 sq cm ,find the height.
8
93ABCD 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
94The 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
95Adjacent 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
96In 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
976.
Find the dimensions of a rectangle with perimeter 16 cm,
whose long side is 3 times its short side.
6
98A 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
parallelogram is ( 45 mathrm{cm}, ) find the length of its base.

8
99In 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
100Find the area in square meter of a
parallelogram, whose base is ( 140 mathrm{cm} ) and altitude is ( 20 mathrm{cm} )
8
101The area of a rectangular park is 3100
( m^{2} ) and its breadth is 50 m. The value of
4 times Its perimeter is
8
102The 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
103Find 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
104In 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
105Fill 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
106Which 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
107Find the perimeter of trapezium if The length of sides of trapezium are
( 25,11,15,13 c m )
8
108A 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
109The 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
110Given 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
111OPQR 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
112The 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
113In 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
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
11565. 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
116The 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
117The 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
118If 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
120The 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
121The 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
122Find the area of the following triangles.8
123Find the area of the triangle for the following
(i) base ( =6 mathrm{cm}, ) height ( =8 mathrm{cm} )
8
124The 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
125The shaded shape is made of 5 congruent squares. The side of one square is ( 4 mathrm{cm} ). Find the total area of the
8
126One 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
127In 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
128Look at the measures shown in the
adjacent figure and find the area of ( square P Q R S )
8
129Twenty 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
130Find the area of parallelogram in which base is ( 2.5 mathrm{cm}, ) and altitude is ( 1.4 mathrm{cm} )8
131A 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
132A 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
133The 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
134The 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
135The 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
13656. 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
137Find the area of the following
parallelogram
8
138n 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
139Find the area of the shaded region in the
figure shown.
8
140A 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
141Calculate 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
142Find 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
143A 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
144Draw 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
145The area of rhombus whose diagonals
are ( 16 mathrm{cm}, 24 mathrm{cm} )
8
146A 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
147Find 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
148Calculate 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
149The 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
150If each edge of a cube is tripled, then find how many times will its volume become?8
151The perimeter of a rhombus is ( 46 mathrm{cm} . ) If
the height of the rhombus is ( 8 mathrm{cm} ); find
its area.
8
152Find the ( z- ) score that corresponds to
the ( 65^{t h} ) percentille of the standard Normal curve.
8
153The 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
154ABCD 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
155Draw 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
156The 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
158A 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
159Find the area of ( | g m A B C D ) if the area
of shaded region is ( 12 mathrm{cm}^{2} )
8
160The 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
161The 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
162A 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
163Find the area of a rhombus whose side
is ( 5 mathrm{cm} ) and whose altitude is ( 4.8 mathrm{cm} )
8
164Find 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
165If 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
166The 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
167Find 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
8
168Rohit’s family is planning to build a
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
169Find 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
170ABCD 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
171The 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
172BD 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
173In 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
174Find the area of trapezium ( boldsymbol{A B C D} )8
175The 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
176Find 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
178Which 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.
A . True
B. False

8
179Calculate 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
180Find the area of a square, the length of
whose diagonal is ( 25 mathrm{cm} )
8
181A rectangular plot is 125 m long and
( 72 m ) broad. Find the cost of fencing it
at ( R s 27 ) per metre.
8
182A 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
183The 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
184A 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
185Calculate 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
186Find the area of the following parallelogram8
187Find the area of rhombus if the base is
( 20 c m ) and height is ( 45 c m )
8
188A 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
189Given ( 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
190The area of quadrilateral constructed by lines ( |boldsymbol{x}|+|boldsymbol{y}|=mathbf{1} ) is
( A cdot 4 )
B. 3
( c cdot 2 )
D.
8
191The 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
19275 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
193The 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
194Edge 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
195Radius of circle is ( 7 mathrm{cm} ) Find Perimeter
and area of circle
8
196The 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
197Find sides a cube is ( 17.5 mathrm{cm} ) find volum
of cube
8
198If 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
199The 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
200What 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
201The 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
202A 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
203Find 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
204The 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
205A 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
206The 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
207In 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
208In 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
209The 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
210A 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
211Find the volume of a cube of side ( 9 mathrm{cm} )
in cubic metres
8
212Two 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
213A square and an equilateral triangle have same perimeters. If diagonal of square is ( 12 sqrt{2} c m, ) then side of traingle
is
8
214A 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
215In 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
216A municipal corporation wall on road side has dimensions as shown in figure
The wall is to be used for
of ( R s .400 ) per ( m^{2} ) in a year. Find the
total amount of revenue earned in a
year.
8
217The 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
219The 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
220Priya 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
222The 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
four points are
( A cdot 28 )
в. 36
( c cdot 48 )
( D )
8
223Find 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
224A 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
225Calculate 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
226The 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
227The 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
228If 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
229In 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
230Each 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
231Two 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
232Tanya 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
234Find 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
236Edge 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
237If each edge of a cube is doubled, how
many times will its volume increase?
8
238The 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
239Find the area of the given parallelogram8
240Given 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
242A 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
243If the volume of a cube is ( 512 mathrm{cm}^{3} ), then
find the length of an edge of the cube
8
244If ( 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
245In 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
246The 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
247The perimeter of rhombus is 52 sq. cm. If one of its diagonal is ( 24 mathrm{cm} ; ) find the length of its other diagonal.8
248If 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
249The 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
251A 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
252A 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
253The measurement of a compass-boxis
( 16 c m times 4 c m times 2 c m, ) find the volume of
a compass-box.
8
254A 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
255A 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
256A 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
257An 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
258One 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
260Circule 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
261Find the area of parallelogram whose
base is ( 48 mathrm{cm} ) and height is ( 25 mathrm{cm} )
8
262State the whether given statement is true or false

Show that area of a rhombus is half the product of the length of its diagonals.
A. True
B. False

8
26366. In A ABC, O is the centroid and
AD, BE, CF are three medians
and the area of A AOE = 15 cm2.
is
(1) 20 cm
(3) 40 cm
(2) 30 cm
(4) 25 cm2
8
264ABCDEF 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
265Area 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
266For 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
267If 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
268All rhombuses are parallelogram.
A. True
B. False
8
269Volume 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
270If ( 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
271The 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
272If 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
273In 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
274The 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
275Food 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
276Calculate the area bounded by the line
( x+y=10 ) and both the coordinates
axes.
8
277The 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
278Find 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
279In fig. ( A B C D ) is a field in the form of a
in the figure. if ( angle D A B=90^{circ}, ) find the
area of the field.
State whether answer given is true or
not
A. True
B. False
8
280One 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
281If the perimeter of one of the faces of a
cube is ( 40 mathrm{cm} ), then what is its volume?
8
282If ( 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
284Find 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
285The 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
286ABCD 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
28767. 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
288If 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
289Find 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
29056. 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
291Find 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
29256. 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
293The area of parallelogram with
diagonals ( 6 mathrm{cm}, 10 mathrm{cm} ) is
8
294Of 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
295The 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
296Area of a parallelogram is ( 400 mathrm{cm}^{2} ) and its height is ( 16 mathrm{cm} . ) Find its base.8
297ABCDEF 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
298Find 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
299Find 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
301mrs 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
302If the number of diagonals in a polygon
is 44 then find its number of sides.
8
303The 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
304If the area of a triangle is 81 square ( mathrm{cm} ) and its perimeters is ( 27 mathrm{cm} ), them its in
A. ( 6 mathrm{cm} )
B. 3 ( mathrm{cm} )
c. ( 1.5 mathrm{cm} )
D. none of these
8
305Four 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
306Two 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
307From 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
308In the figure ( 1, ) find the area of the
parallelogram
8
309The area of a rhombus is ( 48 mathrm{cm}^{2} ). and its
perimeter is ( 20 mathrm{cm} . ) What is its length?
8
310The 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
311The 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
312Find 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
314In 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
315Two 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
316In 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
317External 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
318If the perimeter of the square carpet is
( 100 m, ) find the area covered by the
carpet.
8
319The 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
320Find the area of the following
parallelogram
8
321A 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
322The 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
323A 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
324Find 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
325The 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
326The formula for volume of cube is
A ( cdot l^{3} )
B. ( 6 l^{2} )
c. ( 4 l^{3} )
D. ( 6 l^{3} )
8
327Find the area of the shaded region8
328Calculate the area of the adjoining
figure shown
8
329In 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
330There 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
331A 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
332Show 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
333The 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
334The 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
335OPQR 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
336Find the perimeter of a square which
has an area of ( 121 mathrm{cm}^{2} )
8
337Find 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
338A trapezium PQRSPQRS. Meassuremnt
in centimeters are given as shown in
the figure. Find the area of the
trapezium.
8
339Let ( 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
340In 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
341The perimeter of a rectangle is ( 13 mathrm{cm} ) and its width is ( 2 frac{3}{4} mathrm{cm} . ) Find its length.8
342Find the fourth vertex of the rhombus
formed by (-1,-1),(6,1) and (8,8)
8
343Find 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
344A 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
345The diagonal of a rhombus are ( 15 mathrm{cm} ) and ( 18 mathrm{m} . ) Find its area and side.8
346The 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
347If 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
348In 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
349The 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
350Find 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
351If the diagonals of a parallelogram are
equal, it is a
A. rectangle
B. square
c. trapezium
D. none of these
8
352The 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
353The figure shows Ghanshyam’s squareshaped field. Find the perimeters of the
cabbage and cauliflower patches. Are
they equal?
8
354The 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
355The following figures ( G U N S )
Find ( x text { and } y text { .(Lengths are in } c m) )
8
356Find the area of a rhombus whose
diagonals are ( 12 mathrm{cm} ) and ( 13 mathrm{cm} )
8
357Perimeter 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
358The 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
359DL 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
360A picture frame has dimensions
( 24 mathrm{cm} times 28 mathrm{cm} . ) Find the area of the
picture
8
361A 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
363PQRS 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
364If the side of a rectangle are ( 7 mathrm{cm} ) and
( 5 mathrm{cm}, ) find its area.
8
365The circumference of a circle is ( 22 mathrm{cm} )
Then the area is
8
366Two 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
367If 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
368The 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
369Find the perimeter of each of the following closed figures:
(ii)
8
370If 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
371In 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
372A 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
373Find the area of square with Perimeter
( mathbf{1 0 0 c m} )
8
374Find 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
375If ( 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
376If 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
377The length of a rectangle with area
( 35 c m^{2} ) is ( 7 c m ) What is its breadth.
8
378The 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
379Draw 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
380The 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
381The 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
38370. 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
384In 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
A. 27.5
B . 25
c. 22.5
D. 20
8
385Curved 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
386Find the area of the triangle formed by the line ( 3 x+4 y=12 ) and the ( c o )
ordinate axes.
8
387Perimeter 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
388In 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
389The 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
390The 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
391Show 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
392How 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
393Find the area of a square, if the
measure of its each diagonal is ( 12 mathrm{cm} )
8
394The 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
395The 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
396A 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
397If 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
398A 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
399The length of each side of a square field is ( 63 mathrm{m} ). What is the area of the field?8
400The diagonals of parallelogram are 48 and ( 30 c m ) find its area8
401ABCD 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
402The 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
403Find the area of the quadrilateral ABCD whose vertices are ( A(-3,-1), B(-2,-4) )
( C(4,-1) ) and ( D(3,4) )
8
404A lake on the map has an area of
( 0.15 mathrm{cm}^{2} . ) work out the actual area of the
lake.
8
405In 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
406What 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
407A 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
408A 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
409The 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
410Find the area of the following
trapeziums
8
411Find 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
412The 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 )
A. ( 600 m^{2} )
B. ( 1200 m^{2} )
( mathrm{c} cdot 900 m^{2} )
D. ( 1000 m^{2} )
8
413If the base of a parallelogram decreases
by ( 20 % ), and the height increases by, 40 ( % ) by what percent does the area increase?
8
414The 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
415If 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
416The 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
417Find 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
418Find the area of the following
rhombuses
8
419Two 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
420In 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
421The area of rectangle is ( 540 mathrm{cm} ) and its
length is ( 36 mathrm{cm} ). Find its width and perimeter.
8
422The 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
423The 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
424If 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
425The 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
426A 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
427The 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
428A 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
429The 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
430ABCD 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
432A 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
433Calculate 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
43468. 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
435In 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
436Three 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
437In 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
438Two 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
439A 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
440The 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
441Find 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
442Let ( 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
A . 3
B . 2
( c cdot frac{3}{2} )
( D )
8
443The 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
444Each interior angle of a regular polygon is double of its exterior angle. Find the number of sides in the polygon.8
445The 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
446Consider 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
447The 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
448A 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
449The 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
450Area 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
451From 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
452If (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
453ABCD 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
454Find the area of the given parallelogram8
455A 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
456The area of quadrilateral ABCD given below is 269.2 sq.units
f true then enter 1 and if false then
enter ( mathbf{0} )
8
457PQRS 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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