Perimeter And Area Questions

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

List of perimeter and area Questions

Question No Questions Class
1 A horse is tied to a vertex of a field
having the shape of an equilatera triangle with a rope, the length of which is half of the length of a side of the triangle. The percentage of the total area of the field over which the horse can graze is approximately
A . 20 to 22%
B. 25 to 27%
c. 30 to 32%
D. 48 to 50%		 7
2 Find the area of a quadrant of a circle
whose radius is ( 7 mathrm{cm} )		 7
3 A circular garden has an area of ( 314 m^{2} )
A sprinkle at the centre of garden can
cover an area that has a radius of ( 12 mathrm{m} )
Will the sprinkle water the entire
garden?		 7
4 A postage stamp is ( 12 mathrm{mm} ) in breadth and ( 20 mathrm{mm} ) in length. Find the area of
( operatorname{stamp} operatorname{in} c m^{2} )
A . 0.24
в. 240
c. 24
D. 2.4		 7
5 If the radius of a circle is increased by
( 10 %, ) then the corresponding area of the new circle will be ( ldots(pi=3.14) )
A. ( 121 pi r^{2} )
2
В. ( 12.1 pi r^{2} )
c. ( 1.21 pi^{2} )
D. None of the given three		 7
6 n figure OPQR is a rhombus, three of whose vertices lie on the circle with
centre ( 0 . ) If the area of rhombus is 32
( sqrt{3} mathrm{cm}^{2}, ) find the radius of the circle.
( 4.6 mathrm{cm} )
B. 2 cm
( c .4 mathrm{cm} )
( D )		 7
7 The length, breadth and height of a room are ( 850 mathrm{cm}, 625 mathrm{cm} ) and ( 475 mathrm{cm} )
Find the length of the longest rod that
cam measure the dimensions of the
room exactly.		 7
8 The girth of the roller is ( 75 mathrm{cm} ) and its
width is 2 metres. How many
revolutions must it make to roll a field
whose area is 3 hectare?
A . 2000
B. 20000
( c cdot 200 )
D. NONE OF THESE		 7
9 Is it true to say that area of a segment of a circle is less than the area of its
corresponding sector? Why?
A. yes, it is true for minor segment since ar.minor segment = ar.sector-triangle made by the radii and the chord of the segment.
B. Yes, it is only true for major segment since ar.minor segment = – ar.sector-triangle made by the radii and the chord of the segment
C. No, it is only true for major segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.
D. No, it is only true for minor segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.		 7
10 If the perimeter is half of the area of the
circle numerically then find the radius of the circle.		 7
11 A circle of radius ( 4 mathrm{cm} ) is cut into 6
equal pieces find area of each part		 7
12 n given figure, ABCD is a rectangle, having ( A B=20 mathrm{cm} ) and ( B C=14 mathrm{cm} )
Two sectors of ( 180^{circ} ) have been cut-off.
Calculate the area of the shaded region.		 7
13 The other end of the diameter through
the point (-1,1) on the circle ( x^{2}+ ) ( y^{2}-6 x+4 y-12=0 ) is :
( mathbf{A} cdot(-7,5) )
B. (-7,-5)
c. (7,-5)
D. (7,5)		 7
14 A pond ( 100 m ) in diameter is
surrounded by a circular grass walk
( 2 m ) wide. How many square meters of grass is there on the walk?
( mathbf{A} cdot 98 pi )
в. ( 100 pi )
( c .204 pi )
D. 202pi		 7
15 A path ( 5 mathrm{cm} ) wide runs along inside a
square park of side ( 100 mathrm{cm} ). Find the area of the path. Also find the cost of
cementing at the the rate of Rs 250 per
10 sq.cm.		 7
16 From a piece of cardbord, in the shape
of a trapezium ( A B C D, ) and ( A B | C D )
and ( angle B C D=90^{circ}, ) quarter circle is
removed. Given ( A B=B C=3.5 mathrm{cm} ) and
( D E=2 c m . ) Calculate the area of the
remaining piece of the cardboard (Take
to be ( left.frac{22}{7}right) )		 7
17 Mamta knitted a circular pattern and
then she put a handle around it and
used it as a hand fan. Find the area of
the design she has made, if outer circle
radius is ( 17.5 mathrm{mm} ) and inner circle
radius is ( 7.5 mathrm{mm} .left[boldsymbol{U} boldsymbol{s e} boldsymbol{pi}=frac{22}{7}right] )		 7
18 A wheel takes ( mathrm{m} ) rotations to travel a
certain distance while another whee
whose diameter is four times bigger than it takes n rotations to travel the
same distance. The relation between
A ( cdot m=4 n )
B. ( m=2 n )
( c cdot 2 m=n )
D. ( 4 mathrm{m}=mathrm{n} )		 7
19 In the figure the boundary of the shaded region consists of four semicircular
( operatorname{arcs}, ) the smallest two being equal. If the
diameter of the largest is ( 14 mathrm{cm} ) and of
the smallest is ( 3.5 mathrm{cm}, ) find
1. The length of the boundary
2. The area of the shaded region		 7
20 In the figure, ( O ) is the center of the circle ( angle R P S=40, ) then ( angle O Q P ) is equal to
A .140
в. 130
( c .90 )
( D )		 7
21 Four equal circles describe the four corners of a square such that each touches two of the others. If each side of
the square is ( 14 mathrm{cm} ), then the area
enclosed between the circumferences of
the circle is:
A. 24 sq cm
B. 42 sq ( mathrm{cm} )
c. 154 sq ( mathrm{cm} )
D. 196 sq ( mathrm{cm} )		 7
22 Consider the railway platform which is in square shape having side length ( 2 k m . ) Then area of the platform is 4
A . ( m )
в. ( k m )
( mathrm{c} cdot k m^{2} )
D. ( m^{2} )		 7
23 60. A copper wire is bent in the shape
of a square of area 81cm2. If the
same wire is bent in the form of
a semicircle, the radius (in cm)
of the semicircle is (Take T = 22)
(1) 16 (2) 14
(3) 10
(4) 7 		7
24 The difference between the
circumference and radius of a circle is
( 30 pi . ) Find the diameter of circle.
A. ( frac{30 pi}{2 pi-1} )
в. ( frac{60 pi}{2 pi-1} )
c. ( frac{2 pi-1}{60 pi} )
D. None		 7
25 n Fig. ( P Q R ) is an equilateral
triangle. Arcs have been drawn with
radii ( 14 mathrm{cm} ) each and with centres ( boldsymbol{P}, boldsymbol{Q} )
and ( R ). The area of the shaded region is
A ( cdot 102.6 mathrm{cm}^{2} )
B ( .206 mathrm{cm}^{2} )
( mathbf{c} cdot 308 mathrm{cm}^{2} )
D. ( 345 mathrm{cm}^{2} )		 7
26 A path 7 meters wide surrounds a
circular lawn ( 252 mathrm{m} ) in diameter. Find
the area of path.		 7
27 The cost of fencing a rectangular field at ( R s 18 ) per metre is ( R s 1980 . ) If the
width of the field is ( 23 m ) find its length.		 7
28 In the figure, there are shown sectors of
two concentric circles of radii ( 7 mathrm{cm} ) and
( 3.5 mathrm{cm} . ) Find the area of the shaded region. ( left(boldsymbol{U} boldsymbol{s e} boldsymbol{pi}=frac{boldsymbol{2} boldsymbol{2}}{boldsymbol{7}}right) )
A. 10.425 sq. ( mathrm{cm} )
B. 10.125 sq. ( mathrm{cm} )
c. 9.625 sq. ( mathrm{cm} )
D. 9.152 sq. ( mathrm{cm} )		 7
29 Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is ( 28 mathrm{cm} ) and height is ( 20 mathrm{cm} ). find the approximate area of the sheet required to make a lid of height ( 2 mathrm{cm} ) for this
container.		 7
30 Find the circumference and area of a
circle of radius ( 8.4 mathrm{cm} )		 7
31 A rectangular piece is ( 20 mathrm{m} ) long and 15 ( mathrm{m} ) wide. Form its four corners,
quadrants of radii ( 3.5 mathrm{m} ) have been cut Find the area of the remaining part.		 7
32 The perimeter of a semi-circular protector is ( 72 mathrm{cm} ) then its radius is
( mathrm{cm} )
A . 36
B. 28
( c cdot 14 )
D. 7		 7
33 A floor is ( 5 mathrm{m} ) long and ( 4 mathrm{m} ) wide. ( mathrm{A} ) square carpet of sides ( 3 mathrm{m} ) is laid on the floor. Find the area of the floor that is
not carpeted.		 7
34 The cost of levelling a square lawn at Rs.15 per square meter is ( R s .19,935 )
Find the cost of fencing the lawn at
Rs.22 per meter.		 7
35 EF are
a AD re-
58. If ABCD is a rectangle, E.
the mid-points of BC and A
spectively and G is any poin
EF, then A GAB equals :
v point on
(1)
(rectangle ABCD)
(2)
(rectangle ABCD)
(rectangle ABCD)
5 (rectangle ABCD) 		7
36 The area of a square field is ( 30 frac{1}{4} m^{2} ) Calculate the length of the side of the
square.
A ( cdot_{5} frac{1}{3} m )
в. ( _{5} frac{1}{2} m )
c. ( _{5} frac{2}{5} m )
D. ( _{5} frac{1}{4} m )		 7
37 The area of the shaded region in the given figure is
( A )
в.
c. ( frac{pi}{4} ) sq.units
D. ( pi^{2} ) sq.unis		 7
38 A ( 3 m ) wide path runs outside and
around a rectangular park of length ( 125 m ) and breadth 65 m. Find the area
of the path.		 7
39 Area of a sector of central angle ( 200^{0} ) of
a circle is ( 770 mathrm{cm}^{2} ). The length of the corresponding arc of this sector is
A ( cdot 73 frac{1}{3} c m )
B ( cdot 156 frac{1}{3} c m )
( mathbf{c} cdot 7 frac{1}{3} c m )
D. ( 22 frac{1}{3} ) cm		 7
40 If the outer and inner radii of a ring are
( 10 mathrm{cm} ) and ( 8 mathrm{cm}, ) then its area is nearly
A. 113.443 sq. ( mathrm{cm} )
В. 113.343 sq. ( mathrm{cm} )
c. 113.243 sq. ( mathrm{cm} )
D. 113.143 sq. ( mathrm{cm} )		 7
41 The largest possible square is inscribed
in a circle of circumference ( 2 pi ) units.
The area of the square in square units
is
( mathbf{A} cdot 4 pi sqrt{2} )
В. ( 2 pi sqrt{2} )
( c cdot sqrt{2} )
( D )		 7
42 The minute hand of a clock is ( 10 mathrm{cm} )
long. Find the area of the face of the
clock described by the minute hand between 9 A.M. and 9.35 A.M.		 7
43 Find the area of circle in sq. cms, in which the chord of length ( 18 mathrm{cm} ) is at the distance of half of the radius of circle
from the centre of circle:
A . ( 108 pi )
B. ( 54 pi )
c. ( 27 pi )
D. ( 81 pi )		 7
44 In adjoining fig two semicircles are
drawn on sides ( A D ) and ( B C ) of a square
( A B C D . ) If ( A B=10 mathrm{cm},(pi=3.14) )
then the total area of semicircles is :
A ( .78 .50 mathrm{cm}^{2} )
B. ( 68.50 mathrm{cm}^{2} )
( c cdot 70 mathrm{cm}^{2} )
D. ( 70.48 mathrm{cm}^{2} )		 7
45 A circular park has a path of uniform width around it. The difference between
outer and inner circumference of the
circular path is ( 132 m ). Its width is: Take ( left(boldsymbol{pi}=frac{22}{7}right) )
( A cdot 22 m )
B. ( 20 m )
( mathbf{c} cdot 21 m )
( mathbf{D} cdot 24 m )		 7
46 What is the radius of a circle of area
( 616 mathrm{cm}^{2} ? )
( mathbf{A} cdot 16 mathrm{cm} )
B. ( 12 mathrm{cm} )
( c cdot 14 c m )
D. None of these		 7
47 In the given figure, two connectric circles with centre ( boldsymbol{O} ) have radii ( 21 mathrm{cm} )
and ( 42 mathrm{cm}, ) If ( angle A O B=60^{circ}, ) find the
area of the shaded region ( left[mathbf{U} mathbf{s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] )		 7
48 One side of a square field is 92 m. Find the cost of raising a lawn on the field at
the rate of ( R s .1 .50 ) per ( s q . m )		 7
49 The radius of a circular wheel is ( 1 frac{3}{4} m ) How many revolutions will it make in
traveling ( 11 k m ? )		 7
50 The length and breadth of a rectangular
field are ( 110 m ) and 85 m respectively. Find the perimeter of the field. How
much will it cost to fence the field at the
rate of ( R s 25 ) per metre?		 7
51 From a circular sheet of paper with
radius ( 20 mathrm{cm}, 4 ) circles of radius ( 5 mathrm{cm} )
each are cut out. Find the ratio of the
uncut to the cut portions.
( mathbf{A} cdot 1: 3 )
B. 4: 1
( mathbf{c} cdot 3: 1 )
D. 4: 3		 7
52 Between a square of perimeter ( 44 mathrm{cm} ) and a circle of circumference ( 44 mathrm{cm} ) which figure has a larger area and by how much?
A. Square, ( 33 mathrm{cm}^{2} )
B . Circle, ( 33 mathrm{cm}^{2} )
c. Both have equal areas
D. square, ( 95 mathrm{cm}^{2} )		 7
53 The area of the shaded field shown in
the given figure is:
( mathbf{A} cdot(4 pi+32) mathrm{cm}^{2} )
B ( cdot(2 pi+32) mathrm{cm}^{2} )
( mathbf{c} cdot(2 pi+16) mathrm{cm}^{2} )
( mathbf{D} cdot(4 pi+24) mathrm{cm}^{2} )		 7
54 Find the circumference of the circles
with the following radius:(Take ( pi=frac{22}{7} ) )
( mathbf{1 4 c m} )		 7
55 If the circumference of a circle is
increased by ( 50 % ), by what percent will its area be increased?
A . ( 75 % )
B. ( 100 % )
c. ( 125 % )
D. ( 150 % )		 7
56 Find the circumference of a circle
whose area is ( 301.84 mathrm{cm}^{2} )		 7
57 Area of circle ( A ) is 121 times the area of
circle B. The ratio of the circumference
of circle ( A ) to that of ( B ) is
A . 121:
B. 1: 11
c. 11: 1
D. Cannot be determined		 7
58 10. The length of a rectangle is 6 m less than three times its
breadth. The length and breadth of the rectangle if its
perimeter is 148 m, is
(a) 54 m
(b) 30m
(c) 40m
(d) 20m 		7
59 68. If area of a parallelogram with
sides p and q is R and that of a
rectangle with sides p and qis S,
then :
(1) R>S (2) R<S
(3) R=S (4) None of these 		7
60 Angle in a semicircle is
A. Acute angle
B. Straight angle
C. Right angle
D. Obtuse angle		 7
61 The shape of the top of a table in a
restaurant is that of a segment of a
circle with centre ( O ) and ( angle B O D=90^{circ} )
f ( B O=O D=60 mathrm{cm} . ) The perimeter of
the table is (Take ( pi=mathbf{3 . 1 4} ) )
A . ( 402 mathrm{cm} )
в. ( 402.6 mathrm{cm} )
c. ( 401 mathrm{cm} )
D. ( 400 mathrm{cm} )		 7
62 ABCD is a parallelogram, AD is produced to E so that DE = DC and ED
produced meets AB produced in F. Prove that ( mathrm{BF}=mathrm{BC} )		 7
63 In the figure, from the handkerchief
from four corners, sectors ( P, Q, R ) and ( S )
each of ( 2 mathrm{cm} ) are cut, whose sum is ( boldsymbol{P}+ )
( Q+R+S=A_{1} ) and a circle of
diameter ( 4 mathrm{cm} ) from the centre is cut
whose area is ( A_{2}, ) then is
possible.
A. ( A_{1} neq A_{2} )
B. ( A_{1}A_{2} )
D. ( A_{1}=A_{2} )		 7
64 The area of a circular playground is
( 22176 m^{2} . ) Find the cost of fencing at the
rate of ( R s .50 ) per ( m )		 7
65 Find the circumference of the inner and
the outer circles, shown in the adjoining
figure. (Take ( boldsymbol{pi}=mathbf{3 . 1 4}) )		 7
66 If perimeter of rectangle is equal to perimeter of square,
then side of square is
(a) 60 cm
(b) 18 cm
(c) 225 cm
(d) 15 cm 		7
67 Assertion: The length ofrectangle exceeds its breadth by
4 cm. Iflength and breadth are each increased by 3cm, the
area of the new rectangle will be 81cm- more than that of
given rectangle. Length and breadth are 14 and 10 cm
respectively.
Reason: Area of rectangle=Length x Breadth. 		7
68 Two crossroads,each ( 2 mathrm{m} ) wide,run at
right angles through the center of a rectangular park of length ( 64 mathrm{m} ) and
breadth ( 38 mathrm{m} ),such that each is parallel to one of the sides of the rectangle. Find the area of the roads.also, find the area
of the remaining part of the park		 7
69 In the adjoining figure, ( O A B C ) is a square of side ( 7 mathrm{cm} . O A C ) is a quadrant
of a circle with ( O ) as centre. The area of
the shaded region is
A . ( 10.5 mathrm{cm}^{2} )
В. ( 38.5 mathrm{cm}^{2} )
( mathbf{c} cdot 49 c m^{2} )
D. ( 11.5 mathrm{cm}^{2} )		 7
70 A circular grass lawn of ( 35 m ) in radius
has a path ( 7 m ) wide running around it
on the outside. The area ofthe path is?
A ( cdot 1,496 m^{2} )
B . ( 1,450 m^{2} )
c. ( 1,576 m^{2} )
D. ( 1,694 m^{2} )		 7
71 If we join any two points on a circle
through centre, we get a
A. Radius
B. Diameter
c. chord
D. None of these		 7
72 In the given figure, ( A B C D ) is a piece of
cardboard in the shape of the trapezium
in which ( A B | D C, angle A B C=90^{circ} )
From this piece, quarter circle ( B E F C )
is removed. Given ( D C=B C=4.2 mathrm{cm} )
and ( A E=2 mathrm{cm} . ) Calculate the area of
the remaining piece of the cardboard.
( mathbf{A} cdot 7.98 mathrm{cm}^{2} )
( mathbf{B} cdot 8 mathrm{cm}^{2} )
( mathbf{c} cdot 9.08 mathrm{cm}^{2} )
D. ( 10.08 mathrm{cm}^{2} )		 7
73 Find the circumference of the
semicircle whose diameter is 4 cm.
A. ( 3.46 mathrm{cm} )
B . ( 5.89 mathrm{cm} )
( mathbf{c} cdot 6.28 mathrm{cm} )
D. ( 10.28 mathrm{cm} )		 7
74 8.
The perimeter of a square is
cm. Find the side of the square. 		7
75 The diameter of a wheel of a cycle is 21
cm How far will it go in 28 complete revolutions?
( A cdot 3696 mathrm{cm} )
B. 3669 cm
c. ( 3966 mathrm{cm} )
D. None of these		 7
76 The number of revolutions made by a
wheel of diameter ( 56 mathrm{cm} ) in covering a distance of ( 1.1 k m ) is ( left(U s e pi=frac{22}{7}right) )
( mathbf{A} cdot 31.25 )
B. 56.25
c. 625
D. 62.5		 7
77 51. If the circumference of a circle
30
is , the the diameter of the
T
circle is
(1) 15
T
(3) 60
(4) 30 		7
78 If the ratio of the areas of the two circles
is ( 25: 16, ) then the ratio of their
circumferences is

This question has multiple correct options
A ( cdot frac{625}{500} )
B. ( frac{4}{5} )
( c cdot frac{5}{4} )
D. ( frac{500}{625} )

 7
79 The area of a circle and a square are
equal, the ratio of the sides of the
square to the radius of the circle is
A ( .2: sqrt{pi} )
B. ( sqrt{pi}: 1 )
c. ( sqrt{2}: 1 )
D. ( 1: sqrt{2} )
E . None of these		 7
80 1 LUU
L UPIDU
6
7.
50000
A farmer has one piece of rectangular land measuring 000 m length and 30000 m breadth. If he distributes his land
13
11
among his 5 children, how much area will each child get?
50000 		7
81 The circumference of a circle is ( 100 mathrm{cm} )
Then the side of a square inscribed in the circle is:
A ( cdot frac{100 sqrt{2}}{pi} mathrm{cm} )
B. ( frac{50 sqrt{2}}{pi} mathrm{cm} )
c. ( frac{100}{pi} mathrm{cm} )
D. ( 50 sqrt{2} mathrm{cm} )		 7
82 Which of the following statements are true (T) and which are false (F)?

If all the angles of a quadrilateral are equal, it is a parallelogram.
A . True
B. False

 7
83 A roller of diameter ( 70 mathrm{cm} ) and length
( 2 mathrm{m} ) is rolling on the ground What is the area covered by the roller in 50 revolutions?
A. ( 180 m^{2} )
в. ( 200 m^{2} )
c. ( 220 m^{2} )
D. ( 240 m^{2} )		 7
84 The ratio of the outer and inner
perimeters of a circular path is 23: 22
If the path is ( 5 mathrm{m} ) wide what is the diameter of the circle? Also find the
area of path enclosed between the two
circles.
A. 3535.71 sq. ( mathrm{m} )
B . 1232.23 sq. ( mathrm{m} )
c. 2727.53 sq. ( mathrm{m} )
D. 4343.12 sq. ( mathrm{m} )		 7
85 71. The perimeters of five squares
are 24 cm, 32 cm, 40 cm, 76 cm
and 80 cm respectively. The pe-
rimeter of another square equal
in area to sum of the areas of
these squares is
(1) 31 cm (2) 62 cm
(3) 124 cm (4) 961 cm 		7
86 What is the length of ( A B ? )
( mathbf{A} cdot 8 mathrm{cm} )
B. 4.5cm
C. ( 7.35 mathrm{cm} )
D. ( 7.30 mathrm{cm} )		 7
87 The length and breadth of a rectangular
piece of land are ( 500 mathrm{m} ) and ( 300 mathrm{m} ) respectively.
Find the cost of the land, if ( 1 m^{2} ) of the
land costs Rs. 10,000		 7
88 Which of the following statements are true (T) and which are false (F)?
In a parallelogram, the diagonals are equal.
A. True
B. False		 7
89 Four equal circles, each of radius ( a ) touch each other. Show that the area between then is ( frac{6}{7} a^{2} ) (Take ( left.pi=frac{22}{7}right) ) 7
90 The circumference and area of a circle
of diameter ( 91 mathrm{cm} ) are, respectively
A ( cdot 367 mathrm{cm}, 4986.5 mathrm{cm}^{2} )
B . ( 442 mathrm{cm}, 6166.5 mathrm{cm}^{2} )
( mathbf{c} .286 mathrm{cm}, 6506.5 mathrm{cm}^{2} )
D. ( 456 mathrm{cm}, 5466.5 mathrm{cm}^{2} )		 7
91 Find the radius (in ( mathrm{cm} ) ) of a circle,
whose circumference is ( 22 mathrm{m} )		 7
92 The area of a square playground is
256.6404 square metres. Find the length of one side of the playground.
A. 16.04 metres
B. 16.02 metres
c. 16.06 metres
D. 16.08 metres		 7
93 A circular grassy plot of land, ( 42 m ) in diameter, has a path ( 3.5 m ) wide running around it on the outside. Find
the cost of gravelling the path at ( R s .4 )
per square metre
A. ( R s .2002 )
B. Rs.2003
c. ( R s .2004 )
D. ( R s .2000 )		 7
94 ( ln a triangle w i t h ) sides ( a, b ) and ( c, a )
semicircle touching the sides ( A C ) and
( C B ) is inscribed whose diameter lies on
( A B . ) Then, the radius of the semicircle
is :
A ( cdot frac{a}{2} )
в. ( frac{Delta}{s} )
c. ( frac{Delta}{a+b} )
D. ( frac{2 Delta}{a+b} )		 7
95 If ( P Q R S ) is a square, ( A B | S Q, A ) is
midpoint of ( S R ) and ( A C=C B, ) which
one is true?
A. ( S A=B Q )
B. ( P C ) is the bisector of ( angle S P Q )
c. ( P C ) if produced will pass through ( R )
D. All of these		 7

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