In the given figure, ABC is an equilateral triangle which is inscribed inside a circle and whose radius is r. Which of the following is the area of the triangle ?

${\left( {r + DE} \right)^{\frac{1}{2}}}{\left( {r - DE} \right)^{\frac{3}{2}}}$$

${\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^2}$$

${\left( {r - DE} \right)^2}{\left( {r + DE} \right)^2}$$

${\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^{\frac{3}{2}}}$$

The ratio of bases of two triangles is x : y and that of their areas is a : b. Then the ratio of their corresponding altitudes will be :

$\frac{x}{a}$$ : $$\frac{b}{y}$$

$\frac{a}{x}$$ : $$\frac{b}{y}$$

$\frac{x}{a}$$ : $$\frac{b}{y}$$

924 + Mcqs in Area in Arithmetic Ability Page 1 McqOptions

1.	A courtyard is 25 m long and 16 m broad is to be paved with bricks of dimensions 20 cm by 10 cm. What is the total number of bricks required ?
A.	6000 $${\text{ bricks}}$$
B.	8000 $${\text{ bricks}}$$
C.	0000 $${\text{ bricks}}$$
D.	2000 $${\text{ bricks}}$$
Answer» D. 2000 $${\text{ bricks}}$$

Discussion

2.	Four circles having equal radii are drawn with centres at the four corners of a square. Each circle touches the other two adjacent circles. If the remaining area of the square is 168 cm2, what is the size of the radius of the circle ? (in centimetres)
A.	4 centimetres
B.	.4 centimetres
C.	5 centimetres
D.	1 centimetres
Answer» B. .4 centimetres

Discussion

3.	A field in the form of a parallelogram has one side 150 metres and its distance from the opposite side is 80 metres. The cost of watering the field at the rate of 50 paise per square metre is :
A.	s. 3500
B.	s. 5000
C.	s. 6000
D.	s. 7000
Answer» D. s. 7000

Discussion

4.	If the perimeter of a right-angled isosceles triangle is $$\left( {4\sqrt 2+ 4} \right)$$cm, the length of the hypotenuse is :
A.	cm
B.	cm
C.	cm
D.	0 cm
Answer» B. cm

Discussion

5.	In ΔPQR, side PQ = 32 cm and side PR = 25 cm. What is the measure of side QR ?
A.	$4\sqrt {154} $$cm
B.	$2\sqrt {308} $$cm
C.	$4\sqrt {308} $$cm
D.	annot be determined
E.	one of these
Answer» F.

Discussion

6.	The area of a square is twice that of a rectangle. The perimeter of the rectangle is 10 cm. If its length and breadth each is increased by 1 cm, the area of the rectangle become equal to the area of the square. The length of side of the square is :
A.	$2\sqrt 3 $$ cm
B.	$3\sqrt 2 $$ cm
C.	$4\sqrt 3 $$ cm
D.	$12 $$ cm
Answer» B. $3\sqrt 2 $$ cm

Discussion

7.	If the length of the diagonal of a square is 20 cm, then its perimeter must be :
A.	$10\sqrt 2 \,$$ cm
B.	$40 $$ cm
C.	$40\sqrt 2 \,$$ cm
D.	$ 200 $$ cm
Answer» D. $ 200 $$ cm

Discussion

8.	Three boys are standing on a circular boundary of a fountain. They are at equal distance from each other. If the radius of the boundary is 5 m, the shortest distance between any two boys is :
A.	$\frac{{5\sqrt 3 }}{2}m$$
B.	$5\sqrt 3 \,m$$
C.	$\frac{{15\sqrt 3 }}{2}m$$
D.	$\frac{{10\pi }}{3}m$$
Answer» C. $\frac{{15\sqrt 3 }}{2}m$$

Discussion

9.	The minute hand of a clock is 7 cm long. Find the area of the sector made by the minute hand between 7 am and 7.05 am :
A.	1.53 cm2
B.	2.83 cm2
C.	5.43 cm2
D.	one of these
Answer» C. 5.43 cm2

Discussion

10.	Two boys are running ontwo different circular paths with same centre. If their radii are 5 m and 10 m, the maximum possible distance between them is :
A.	m
B.	0 m
C.	5 m
D.	0 m
Answer» D. 0 m

Discussion

11.	The areas of two circular fields are in the ratio 16 : 49. If the radius of the latter is 14 m, the what is the radius of the former ?
A.	m
B.	m
C.	8 m
D.	2 m
Answer» C. 8 m

Discussion

12.	The area of a circular field is equal to the area of a rectangular field. The ratio of the length and the breadth of the rectangular field is 14 : 11 respectively and perimeter is 100 metres. What is the diameter of the circular field ?
A.	4 m
B.	2 m
C.	4 m
D.	8 m
E.	one of these
Answer» E. one of these

Discussion

13.	The cost of cultivating a square field at the rate of Rs. 685 per hector is Rs. 6165. The cost of putting a fence around it at the rate of Rs. 48.75 per metre would be :
A.	s. 23400
B.	s. 52650
C.	s. 58500
D.	s. 117000
Answer» D. s. 117000

Discussion

14.	A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper ?
A.	40 cm2
B.	40 cm2
C.	60 cm2
D.	one of these
Answer» B. 40 cm2

Discussion

15.	A kite-shaped quadrilateral of the largest possible area is cut from a circular sheet of paper. If the lengths of the sides of the kite are in the ratio 3 : 3 : 4 : 4, what percentage of the circular sheet is wasted ?
A.	4%
B.	9%
C.	2%
D.	7%
Answer» C. 2%

Discussion

16.	In the given figure, ABC is an equilateral triangle which is inscribed inside a circle and whose radius is r. Which of the following is the area of the triangle ?
A.	${\left( {r + DE} \right)^{\frac{1}{2}}}{\left( {r - DE} \right)^{\frac{3}{2}}}$$
B.	${\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^2}$$
C.	${\left( {r - DE} \right)^2}{\left( {r + DE} \right)^2}$$
D.	${\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^{\frac{3}{2}}}$$
Answer» E.

Discussion

17.	A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of the second square is :
A.	: 5
B.	: 2
C.	: 5
D.	: 4
Answer» C. : 5

Discussion

18.	The circumference of the back-sided wheel of a vehicle is 1 m greater than that of front side wheel. To travel 600 m, the front wheel rotates 30 times more than the back wheel. The circumference of the front wheel is :
A.	m
B.	m
C.	m
D.	one of these
Answer» C. m

Discussion

19.	If the ratio between the areas of two circles is 4 : 1 then the ratio between their radii will be ?
A.	: 2
B.	: 1
C.	: 3
D.	: 1
Answer» C. : 3

Discussion

20.	A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle ?
A.	8 cm2
B.	54 cm2
C.	250 cm2
D.	annot be determined
E.	one of these
Answer» F.

Discussion

21.	The base and altitude of a right-angled triangle are 12 cm and 5 cm respectively. The perpendicular distance of its hypotenuse from the opposite vertex is :
A.	$4\frac{4}{{13}}\,cm$$
B.	$4\frac{8}{{13}}\,cm$$
C.	$6\frac{9}{{13}}\,cm$$
D.	$5\,cm$$
E.	$7\,cm$$
Answer» C. $6\frac{9}{{13}}\,cm$$

Discussion

22.	The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is $$\frac{3}{2}$$ times that of the side pf the square, then the side if the square is :
A.	5 cm
B.	0 cm
C.	0 cm
D.	0 cm
Answer» C. 0 cm

Discussion

23.	The area of a square is three-fifths the area of a rectangle. The length of the rectangle is 25 cm and its breadth is 10 cm less than its length. What is the perimeter of the square ?
A.	4 cm
B.	0 cm
C.	0 cm
D.	annot be determined
E.	one of these
Answer» C. 0 cm

Discussion

24.	Two sides of a rectangle were measured. One of the sides (length) was measured 10% more than its actual length and the other side (width) was measured 5% less than its actual length. The percentage error in measure obtained for the area of the rectangle is :
A.	.5%
B.	%
C.	.56%
D.	5%
Answer» B. %

Discussion

25.	A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is :
A.	5 m × 6.67 m
B.	0 m × 5 m
C.	0 m × 3.33 m
D.	0 m × 2.5 m
Answer» C. 0 m × 3.33 m

Discussion

26.	There are 4 semi-circular gardens on each side of a square-shaped pond with each side 21 m. The cost of fencing the entire plot at the rate of Rs. 12.50 per metre is :
A.	s. 1560
B.	s. 1650
C.	s. 3120
D.	s. 3300
Answer» C. s. 3120

Discussion

27.	What is the area of the given figure ?
A.	8.8 cm2
B.	10.4 cm2
C.	20 cm2
D.	32.6 cm2
Answer» C. 20 cm2

Discussion

28.	The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less by 3 cm. Find the perimeter of the rectangle ?
A.	7 cm
B.	6 cm
C.	0 cm
D.	4 cm
Answer» E.

Discussion

29.	If the length of diagonal AC of a square ABCD is 5.2 cm, then the area of the square is :
A.	0.52 sq.cm
B.	1.52sq.cm
C.	2.52sq.cm
D.	3.52sq.cm
Answer» E.

Discussion

30.	ABCD is a square and AEFG is a rectangle. Area of each of them is 36 sq.m. E is the mid-point of AB. The perimeter of the rectangle AEFG is :
A.	2 m
B.	8 m
C.	0 m
D.	6 m
Answer» D. 6 m

Discussion

31.	A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is :
A.	0%
B.	0.08%
C.	0%
D.	8%
Answer» E.

Discussion

32.	What will be the area of a semi-circle whose perimeter is 36 cm ?
A.	54 cm2
B.	68 cm2
C.	08 cm2
D.	ata inadequate
E.	one of these
Answer» F.

Discussion

33.	If the perimeter of a square is equal to the radius of a circle whose area is 39424 sq. m. What is the area of the square ?
A.	41 sq.m
B.	84 sq.m
C.	225 sq.m
D.	annot be determined
E.	one of these
Answer» C. 225 sq.m

Discussion

34.	The diameter of a circle is 3.5 cm. What is the circumference of the circle ?
A.	1 cm
B.	2 cm
C.	8.5 cm
D.	5.2 cm
E.	one of these
Answer» B. 2 cm

Discussion

35.	If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area ?
A.	o change
B.	% decrease
C.	6% increase
D.	6% decrease
Answer» E.

Discussion

36.	A triangle of area 9y cm2 has been drawn such that its area is equal to the area of an equilateral triangle of side 6 cm. The value of y would be :
A.	$\sqrt 2 $$
B.	$\sqrt 3 $$
C.	$ 2 $$
D.	$ 3 $$
Answer» C. $ 2 $$

Discussion

37.	The area of a triangle is p sq.cm and its base is x cm. What is the height of the triangle (in cm) ?
A.	$\frac{2p}{x}$$
B.	$\frac{x}{2p}$$
C.	$\frac{p}{2x}$$
D.	$\frac{2x}{p}$$
Answer» B. $\frac{x}{2p}$$

Discussion

38.	If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. The perimeter of the original rectangle (in cm) is :
A.	4
B.	6
C.	8
D.	0
Answer» E.

Discussion

39.	The area of the shaded portion is :
A.	0 sq. cm
B.	4 sq. cm
C.	1 sq. cm
D.	5 sq. cm
Answer» D. 5 sq. cm

Discussion

40.	The area of a square with perimeter 48 cm, is :
A.	44 sq. cm
B.	56 sq. cm
C.	70 sq. cm
D.	75 sq. cm
Answer» B. 56 sq. cm

Discussion

41.	If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in its area will be :
A.	% increase
B.	% decrease
C.	0% increase
D.	o change
Answer» C. 0% increase

Discussion

42.	The area of a rectangle field is 52000 m2 . This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 3.25 cm on the map. The breadth of the rectangular field is :
A.	50 m
B.	60 m
C.	00.5 m
D.	00.5 m
Answer» C. 00.5 m

Discussion

43.	The total surface area of a right circular cylinder with radius of the base 7 cm and height 20 cm, is :
A.	00 cm2
B.	40 cm2
C.	000 cm2
D.	188 cm2
Answer» E.

Discussion

44.	Three equal circles are described with vertices of the triangles as centres. If the radius of each circle is r, the sum of areas of the portions of the circles intercepted in a triangle is :
A.	${2\pi {r^2}}$$
B.	$3\frac{{\pi {r^2}}}{2}$$
C.	${\pi {r^2}}$$
D.	$1\frac{{\pi {r^2}}}{2}$$
Answer» E.

Discussion

45.	What is the area of the shaded region ?
A.	32 - 4π) sq. units
B.	32 - 8π) sq. units
C.	16 - 4π) sq. units
D.	16 - 8π) sq. units
Answer» C. 16 - 4π) sq. units

Discussion

46.	A vertical rod of height 33 metres is bent to form a semi-circular shape so that the top touches the ground. The distance between the top head and the base on the ground is :
A.	0.5 m
B.	2 m
C.	1 m
D.	3 m
Answer» D. 3 m

Discussion

47.	The ratio of bases of two triangles is x : y and that of their areas is a : b. Then the ratio of their corresponding altitudes will be :
A.	$ax : by$$
B.	$\frac{a}{x}$$ : $$\frac{b}{y}$$
C.	$ay : bx$$
D.	$\frac{x}{a}$$ : $$\frac{b}{y}$$
Answer» D. $\frac{x}{a}$$ : $$\frac{b}{y}$$

Discussion

48.	The length, breadth and height of the room are in the ratio 3 : 2 : 1. The breadth and height of the room are halved and length of the room is doubled. The area of the four walls of the room will :
A.	ecrease by 13.64%
B.	ecrease by 15%
C.	ecrease by 18.75%
D.	ecrease by 30%
Answer» E.

Discussion

49.	The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :
A.	5%
B.	2%
C.	2%
D.	2%
Answer» E.

Discussion

50.	Perimeter of a rectangular field is 160 metres and the difference between its two adjacent sides is 48 metres. The side of a square field, having the same area as that of the rectangle, is :
A.	metres
B.	metres
C.	6 metres
D.	2 metres
Answer» E.

Discussion

Explore topic-wise MCQs in Arithmetic Ability.

A courtyard is 25 m long and 16 m broad is to be paved with bricks of dimensions 20 cm by 10 cm. What is the total number of bricks required ?

Four circles having equal radii are drawn with centres at the four corners of a square. Each circle touches the other two adjacent circles. If the remaining area of the square is 168 cm2, what is the size of the radius of the circle ? (in centimetres)

A field in the form of a parallelogram has one side 150 metres and its distance from the opposite side is 80 metres. The cost of watering the field at the rate of 50 paise per square metre is :

If the perimeter of a right-angled isosceles triangle is $$\left( {4\sqrt 2+ 4} \right)$$cm, the length of the hypotenuse is :

In ΔPQR, side PQ = 32 cm and side PR = 25 cm. What is the measure of side QR ?

The area of a square is twice that of a rectangle. The perimeter of the rectangle is 10 cm. If its length and breadth each is increased by 1 cm, the area of the rectangle become equal to the area of the square. The length of side of the square is :

If the length of the diagonal of a square is 20 cm, then its perimeter must be :

Three boys are standing on a circular boundary of a fountain. They are at equal distance from each other. If the radius of the boundary is 5 m, the shortest distance between any two boys is :

The minute hand of a clock is 7 cm long. Find the area of the sector made by the minute hand between 7 am and 7.05 am :

Two boys are running ontwo different circular paths with same centre. If their radii are 5 m and 10 m, the maximum possible distance between them is :

The areas of two circular fields are in the ratio 16 : 49. If the radius of the latter is 14 m, the what is the radius of the former ?

The area of a circular field is equal to the area of a rectangular field. The ratio of the length and the breadth of the rectangular field is 14 : 11 respectively and perimeter is 100 metres. What is the diameter of the circular field ?

The cost of cultivating a square field at the rate of Rs. 685 per hector is Rs. 6165. The cost of putting a fence around it at the rate of Rs. 48.75 per metre would be :

A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper ?

A kite-shaped quadrilateral of the largest possible area is cut from a circular sheet of paper. If the lengths of the sides of the kite are in the ratio 3 : 3 : 4 : 4, what percentage of the circular sheet is wasted ?

In the given figure, ABC is an equilateral triangle which is inscribed inside a circle and whose radius is r. Which of the following is the area of the triangle ?

A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of the second square is :

The circumference of the back-sided wheel of a vehicle is 1 m greater than that of front side wheel. To travel 600 m, the front wheel rotates 30 times more than the back wheel. The circumference of the front wheel is :

If the ratio between the areas of two circles is 4 : 1 then the ratio between their radii will be ?

A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle ?

The base and altitude of a right-angled triangle are 12 cm and 5 cm respectively. The perpendicular distance of its hypotenuse from the opposite vertex is :

The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is $$\frac{3}{2}$$ times that of the side pf the square, then the side if the square is :

The area of a square is three-fifths the area of a rectangle. The length of the rectangle is 25 cm and its breadth is 10 cm less than its length. What is the perimeter of the square ?

Two sides of a rectangle were measured. One of the sides (length) was measured 10% more than its actual length and the other side (width) was measured 5% less than its actual length. The percentage error in measure obtained for the area of the rectangle is :

A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is :

There are 4 semi-circular gardens on each side of a square-shaped pond with each side 21 m. The cost of fencing the entire plot at the rate of Rs. 12.50 per metre is :

What is the area of the given figure ?

The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less by 3 cm. Find the perimeter of the rectangle ?

If the length of diagonal AC of a square ABCD is 5.2 cm, then the area of the square is :

ABCD is a square and AEFG is a rectangle. Area of each of them is 36 sq.m. E is the mid-point of AB. The perimeter of the rectangle AEFG is :

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is :

What will be the area of a semi-circle whose perimeter is 36 cm ?

If the perimeter of a square is equal to the radius of a circle whose area is 39424 sq. m. What is the area of the square ?

The diameter of a circle is 3.5 cm. What is the circumference of the circle ?

If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area ?

A triangle of area 9y cm2 has been drawn such that its area is equal to the area of an equilateral triangle of side 6 cm. The value of y would be :

The area of a triangle is p sq.cm and its base is x cm. What is the height of the triangle (in cm) ?

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. The perimeter of the original rectangle (in cm) is :

The area of the shaded portion is :

The area of a square with perimeter 48 cm, is :

If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in its area will be :

The area of a rectangle field is 52000 m2 . This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 3.25 cm on the map. The breadth of the rectangular field is :

The total surface area of a right circular cylinder with radius of the base 7 cm and height 20 cm, is :

Three equal circles are described with vertices of the triangles as centres. If the radius of each circle is r, the sum of areas of the portions of the circles intercepted in a triangle is :

What is the area of the shaded region ?

A vertical rod of height 33 metres is bent to form a semi-circular shape so that the top touches the ground. The distance between the top head and the base on the ground is :

The ratio of bases of two triangles is x : y and that of their areas is a : b. Then the ratio of their corresponding altitudes will be :

The length, breadth and height of the room are in the ratio 3 : 2 : 1. The breadth and height of the room are halved and length of the room is doubled. The area of the four walls of the room will :

The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :

Perimeter of a rectangular field is 160 metres and the difference between its two adjacent sides is 48 metres. The side of a square field, having the same area as that of the rectangle, is :