In a triangle ABC, a line XY is drawn parallel to BC meeting AB in X and AC in Y. The area of the triangle AXY is half of the area of the triangle ABC. XY divides AB in the ratio of :

$\sqrt 2 :\left( {\sqrt 2- 1} \right)$$

$1:\left( {\sqrt 2- 1} \right)$$

924 + Mcqs in Area Page 3 McqOptions

101.	A rectangular garden (60 m × 40 m) is surrounded by a road of width 2 m, the road is covered by tiles and the garden is fenced. If the total expenditure is Rs. 51600 and rate of fencing is Rs. 50 per metre, then the cost of covering 1 sq. m of road by tiles is :
A.	s. 10
B.	s. 50
C.	s. 100
D.	s. 150
Answer» D. s. 150

Discussion

102.	A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :
A.	m
B.	2 m
C.	3 m
D.	4.5 m
Answer» C. 3 m

Discussion

103.	The area of a rectangle is 252 cm2 and its length and breadth are in the ratio of 9 : 7 respectively. What is its perimeter ?
A.	4 cm
B.	8 cm
C.	6 cm
D.	28 cm
Answer» B. 8 cm

Discussion

104.	ABCD is a square. E is the mid-point of BC and F is the mid-point of CD. The ratio of the area of triangle AEF to the area of the square ABCD is :
A.	: 2
B.	: 3
C.	: 4
D.	: 8
Answer» E.

Discussion

105.	The sides of a triangle are consecutive integers. The perimeter of the triangle is 120 cm. Find the length of the greatest side :
A.	9 cm
B.	0 cm
C.	1 cm
D.	2 cm
Answer» D. 2 cm

Discussion

106.	The dimensions of a room are 12.5 metres by 9 metres by 7 metres. There are 2 doors and 4 windows in the room; each door measures 2.5 metres by 1.2 metres and each window 1.5 metres by 1 metre. Find the cost of painting the walls at Rs. 3.50 per square metre.
A.	s. 150.50
B.	s. 1011.50
C.	s. 1101.50
D.	annot be determined
Answer» C. s. 1101.50

Discussion

107.	Of the two square fields, the area of one is 1 hectare while the other one is broader by 1%. The difference in their areas is :
A.	00 m2
B.	01 m2
C.	00 m2
D.	01 m2
Answer» E.

Discussion

108.	The length and breadth of the floor of the room are 20 feet and 10 feet respectively. Square tiles of 2 feet length of different colours are to be laid on the floor. Black tiles are laid in the first row on all sides. If white tiles are laid in the one-third of the remaining and blue tiles in the rest, how many blue tiles will be there ?
A.	6
B.	4
C.	2
D.	8
E.	one of these
Answer» B. 4

Discussion

109.	A path of uniform width runs round the inside of a rectangular field 38 m long32 m wide. If the path occupies 600 m2, then the width of the path is :
A.	m
B.	0 m
C.	8.75 m
D.	0 m
Answer» B. 0 m

Discussion

110.	If the diagonal and the area of a rectangle are 25 m2and 168 m2, what is the length of the rectangle ?
A.	2 m
B.	7 m
C.	4 m
D.	1 m
Answer» D. 1 m

Discussion

111.	A man is walking in a rectangular field whose perimeter is 6 km. If the area of the rectangular field be 2 sq. km, then what is the difference between the length and breadth of the rectangle ?
A.	$\frac{1}{2}\,km$$
B.	$1\,km$$
C.	$1\frac{1}{2}\,km$$
D.	$2\,km$$
Answer» C. $1\frac{1}{2}\,km$$

Discussion

112.	If the total surface area of a cube is 864 square cm, find the volume of the cube ?
A.	728 cm3
B.	624 cm3
C.	44 cm3
D.	684 cm3
Answer» B. 624 cm3

Discussion

113.	Area of a rectangle is 150 sq. metre. When the breadth of the same rectangle is increased by 2 metres and the length decreased by 5 metres the area of the rectangle decreases by 30 square metres. What is the perimeter of the square whose sides are equal to the length of the rectangle ?
A.	6 m
B.	2 m
C.	20 m
D.	0 m
Answer» E.

Discussion

114.	A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before, is :
A.	0 min
B.	5 min
C.	0 min
D.	00 min
Answer» D. 00 min

Discussion

115.	The sides of a rectangle are 8 cm and 6 cm. The corners of the rectangle lie on a circle. Find the are a of the circle without the rectangle :
A.	0.6 cm2
B.	9 cm2
C.	2.4 cm2
D.	5.3 cm2
Answer» B. 9 cm2

Discussion

116.	A circular swimming pool is surrounded by a concrete wall 4 ft. wide. If the area of the concrete wall surrounding the pool is $$\frac{{11}}{{25}}$$ that of the pool, then the radius of the pool is :
A.	ft
B.	6 ft
C.	0 ft
D.	0 ft
Answer» D. 0 ft

Discussion

117.	If the wheel of the engine of a train $$4\frac{2}{7}$$ metres in circumference makes 7 revolutions in 4 seconds, then the speed (in km/hr) of the train is :
A.	7
B.	8
C.	9
D.	0
Answer» B. 8

Discussion

118.	Two small circular parks of diameters 16 m and 12 m are to be replaced by a Bigger circular park. What would be the radius of this new park. If the new park has to occupy the same space as the two small parks ?
A.	0 m
B.	5 m
C.	0 m
D.	5 m
Answer» B. 5 m

Discussion

119.	If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is :
A.	reater than 1
B.	qual to 1
C.	qual to $$\frac{1}{2}$$
D.	qual to $$\frac{1}{4}$$
Answer» C. qual to $$\frac{1}{2}$$

Discussion

120.	If x is the length of a median of an equilateral triangle, then its area is :
A.	2
B.	$\frac{1}{2}{x^2}$$
C.	$\frac{{\sqrt 3 }}{2}{x^2}$$
D.	$\frac{{\sqrt 3 }}{3}{x^2}$$
Answer» E.

Discussion

121.	The sides of a triangle are in ratio of $$\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$$. If the perimeter is 52 cm, then the length of the smallest side is :
A.	cm
B.	0 cm
C.	1 cm
D.	2 cm
Answer» E.

Discussion

122.	The length of a room is double its breadth. The cost of colouring the ceiling at Rs. 25 per sq. meter is Rs. 5000 and the cost of painting the four walls at Rs. 240 per sq. metre is Rs. 64800. Find the height of the room :
A.	.5 m
B.	m
C.	.5 m
D.	m
Answer» D. m

Discussion

123.	If a square of area $$\frac{\text{A}}{2}$$ is cut off from a given square of area A, then the ratio of diagonal of the cut off square to that of the given square is :
A.	: 5
B.	: $$2\sqrt 5 $$
C.	: $$\sqrt 5 $$
D.	: $$\sqrt 2 $$
Answer» E.

Discussion

124.	How many squares with side $$\frac{1}{2}$$ inch long are needed to cover a rectangle that is 4 feet long and 6 feet wide ?
A.	4
B.	6
C.	456
D.	3824
E.	2466
Answer» E. 2466

Discussion

125.	The breadth of a rectangular field is $$\frac{3}{4}$$ of its length and its area is 300 sq. metres. What will be the area (in sq. metres) of the garden of breath 1.5 metres developed around the field ?
A.	6 m2
B.	05 m2
C.	14 m2
D.	annot be determined
E.	one of these
Answer» D. annot be determined

Discussion

126.	The diagonal of a rectangle is $$\sqrt {41} $$ cm and its area is 20 sq. cm. The perimeter of the rectangle must be :
A.	cm
B.	8 cm
C.	0 cm
D.	1 cm
Answer» C. 0 cm

Discussion

127.	The perimeter of a rectangle is 60 metres. If its length is twice its breadth, then its area is :
A.	60 m2
B.	80 m2
C.	00 m2
D.	20 m2
Answer» D. 20 m2

Discussion

128.	What would be the area of a rectangle whose area is equal to the area of a circle of radius 7 cm ?
A.	7 cm2
B.	54 cm2
C.	84 cm2
D.	80 cm2
Answer» C. 84 cm2

Discussion

129.	A plate on square base made of brass is of length x cm and width 1 mm. The plate weights 4725 gm. If 1 cubic cm cm of brass weight 8.4 grams, then the value of x is :
A.	5
B.	6
C.	2
D.	4
Answer» B. 6

Discussion

130.	If the radius of a circle is increased by 75%, then its circumference will increase by :
A.	5%
B.	0%
C.	5%
D.	00%
Answer» D. 00%

Discussion

131.	The area of the largest circle, that can be drawn inside a rectangle with side 18 cm by 14 cm, is :
A.	9 cm2
B.	54 cm2
C.	78 cm2
D.	078 cm2
Answer» C. 78 cm2

Discussion

132.	The area of a grassy plot is 480 sq. m. If each side had been 5 m longer, the area would have been increased by 245 sq. m. Find the length of the fence to surround it.
A.	7 m
B.	8 m
C.	0 m
D.	one of these
Answer» C. 0 m

Discussion

133.	The perimeter of a rectangular field is 480 metres and the ratio between the length and the breadth is 5 : 3. The area is :
A.	350 sq. m
B.	550 sq. m
C.	3500 sq. m
D.	5500 sq. m
Answer» D. 5500 sq. m

Discussion

134.	The perimeter of a square and a regular hexagon are equal. The ratio of the area of the hexagon to the area of the square is :
A.	$2\sqrt 3 :1$$
B.	$2\sqrt 3 :3$$
C.	$3\sqrt 3 :2$$
D.	$\sqrt 2 :3$$
Answer» C. $3\sqrt 3 :2$$

Discussion

135.	The ratio of circumference and diameter of a circle is 22 : 7. If the circumference be $$1\frac{4}{7}$$ m, then the radius of the circle is :
A.	$\frac{1}{3}\,m$$
B.	$\frac{1}{2}\,m$$
C.	$\frac{1}{4}\,m$$
D.	$1m$$
Answer» D. $1m$$

Discussion

136.	If the circumference of a circle is increased by 20%, what will be the effect on the circle ?
A.	0% increase
B.	4% increase
C.	8% increase
D.	annot be determined
E.	one of these
Answer» C. 8% increase

Discussion

137.	A circle is circumscribed around a square as shown in the figure. The area of one of the four shaded portions is equal to $$\frac{4}{7}$$. The radius of the circle is :
A.	$\sqrt 2 $$
B.	$\frac{1}{{\sqrt 2 }}$$
C.	$2$$
D.	$3$$
Answer» B. $\frac{1}{{\sqrt 2 }}$$

Discussion

138.	The area of a circle is increased by 22 sq. cm if its radius is increased by 1 cm. The original radius of the circle is :
A.	cm
B.	.2 cm
C.	.5 cm
D.	cm
Answer» B. .2 cm

Discussion

139.	Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is :
A.	2 cm/sec
B.	4 cm/sec
C.	6 cm/sec
D.	32 cm/sec
Answer» B. 4 cm/sec

Discussion

140.	A circular pond has area equal to 616 m2. A circular stage is made at the centre of the pond whose radius is equal to half the radius of the pond. What is the area where water is present ?
A.	54 sq. m
B.	62 sq. m
C.	32 sq. m
D.	64 sq. m
Answer» C. 32 sq. m

Discussion

141.	ABCD is a rectangle and E and F are the mid-points of AD and DC respectively. Then the ratio of the areas of EDF and AEFC would be :
A.	: 2
B.	: 3
C.	: 4
D.	: 3
Answer» C. : 4

Discussion

142.	A rectangular farm has to be fenced on one long side, one short side and the diagonal. If the cost of fencing is Rs. 100 per m, the area of the farm is 1200 m2 and the short side is 30 m long, how much would the job cost ?
A.	s. 7000
B.	s. 12000
C.	s. 14000
D.	s. 15000
Answer» C. s. 14000

Discussion

143.	A hall 50 m long and 45 m broad is to be paved with square tiles. Find the largest tile as well as its number in the given options so that the tiles exactly fit in the hall :
A.	6 sq. m and 80 tiles
B.	6 sq. m and 80 tiles
C.	5 sq. m and 90 tiles
D.	6 sq. m and 90 tiles
Answer» D. 6 sq. m and 90 tiles

Discussion

144.	If an equilateral triangle of area X and a square of area Y have the same perimeter, then X is :
A.	qual to Y
B.	reater than Y
C.	ess than Y
D.	ess than or equal to Y
Answer» D. ess than or equal to Y

Discussion

145.	In a triangle ABC, a line XY is drawn parallel to BC meeting AB in X and AC in Y. The area of the triangle AXY is half of the area of the triangle ABC. XY divides AB in the ratio of :
A.	$1:\sqrt 2 $$
B.	$\sqrt 2 :\left( {\sqrt 2- 1} \right)$$
C.	$1:\left( {\sqrt 2- 1} \right)$$
D.	$\sqrt 2 :\sqrt 3 $$
Answer» D. $\sqrt 2 :\sqrt 3 $$

Discussion

146.	A hall, whose length is 16 m and the breadth is twice its height, takes 168 m of paper with 2 m as its width to cover its four walls. The area of the floor is :
A.	6 m2
B.	90 m2
C.	92 m2
D.	16 m2
Answer» D. 16 m2

Discussion

147.	If the sides of a square be double find the increase of percentage in area :
A.	00%
B.	00%
C.	00%
D.	00%
Answer» D. 00%

Discussion

148.	Three plots having areas 110, 130 and 190 square metres are to be subdivided into flower beds of equal size. If the breadth of a bed is 2 metres, the maximum length of a bed van be :
A.	m
B.	1 m
C.	3 m
D.	9 m
Answer» B. 1 m

Discussion

149.	A rectangular lawn 80 metres by 60 metres has two roads each 10 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at Rs. 30 per square metre.
A.	s. 3600
B.	s. 3900
C.	s. 36000
D.	s. 39000
Answer» E.

Discussion

150.	The length of a rectangular blackboard is 8 m more than its breadth. If its length is increased by 7 m and its breadth is decreased by 4 m, its area remains unchanged. The length and breadth of the rectangular blackboard is :
A.	4 m, 16 m
B.	0 m, 24 m
C.	8 m, 16 m
D.	8 m, 20 m
Answer» E.

Discussion

Explore topic-wise MCQs in Arithmetic Ability.

A rectangular garden (60 m × 40 m) is surrounded by a road of width 2 m, the road is covered by tiles and the garden is fenced. If the total expenditure is Rs. 51600 and rate of fencing is Rs. 50 per metre, then the cost of covering 1 sq. m of road by tiles is :

A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :

The area of a rectangle is 252 cm2 and its length and breadth are in the ratio of 9 : 7 respectively. What is its perimeter ?

ABCD is a square. E is the mid-point of BC and F is the mid-point of CD. The ratio of the area of triangle AEF to the area of the square ABCD is :

The sides of a triangle are consecutive integers. The perimeter of the triangle is 120 cm. Find the length of the greatest side :

The dimensions of a room are 12.5 metres by 9 metres by 7 metres. There are 2 doors and 4 windows in the room; each door measures 2.5 metres by 1.2 metres and each window 1.5 metres by 1 metre. Find the cost of painting the walls at Rs. 3.50 per square metre.

Of the two square fields, the area of one is 1 hectare while the other one is broader by 1%. The difference in their areas is :

A path of uniform width runs round the inside of a rectangular field 38 m long32 m wide. If the path occupies 600 m2, then the width of the path is :

If the diagonal and the area of a rectangle are 25 m2and 168 m2, what is the length of the rectangle ?

A man is walking in a rectangular field whose perimeter is 6 km. If the area of the rectangular field be 2 sq. km, then what is the difference between the length and breadth of the rectangle ?

If the total surface area of a cube is 864 square cm, find the volume of the cube ?

Area of a rectangle is 150 sq. metre. When the breadth of the same rectangle is increased by 2 metres and the length decreased by 5 metres the area of the rectangle decreases by 30 square metres. What is the perimeter of the square whose sides are equal to the length of the rectangle ?

A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before, is :

The sides of a rectangle are 8 cm and 6 cm. The corners of the rectangle lie on a circle. Find the are a of the circle without the rectangle :

A circular swimming pool is surrounded by a concrete wall 4 ft. wide. If the area of the concrete wall surrounding the pool is $$\frac{{11}}{{25}}$$ that of the pool, then the radius of the pool is :

If the wheel of the engine of a train $$4\frac{2}{7}$$ metres in circumference makes 7 revolutions in 4 seconds, then the speed (in km/hr) of the train is :

Two small circular parks of diameters 16 m and 12 m are to be replaced by a Bigger circular park. What would be the radius of this new park. If the new park has to occupy the same space as the two small parks ?

If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is :

If x is the length of a median of an equilateral triangle, then its area is :

The sides of a triangle are in ratio of $$\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$$. If the perimeter is 52 cm, then the length of the smallest side is :

The length of a room is double its breadth. The cost of colouring the ceiling at Rs. 25 per sq. meter is Rs. 5000 and the cost of painting the four walls at Rs. 240 per sq. metre is Rs. 64800. Find the height of the room :

If a square of area $$\frac{\text{A}}{2}$$ is cut off from a given square of area A, then the ratio of diagonal of the cut off square to that of the given square is :

How many squares with side $$\frac{1}{2}$$ inch long are needed to cover a rectangle that is 4 feet long and 6 feet wide ?

The breadth of a rectangular field is $$\frac{3}{4}$$ of its length and its area is 300 sq. metres. What will be the area (in sq. metres) of the garden of breath 1.5 metres developed around the field ?

The diagonal of a rectangle is $$\sqrt {41} $$ cm and its area is 20 sq. cm. The perimeter of the rectangle must be :

The perimeter of a rectangle is 60 metres. If its length is twice its breadth, then its area is :

What would be the area of a rectangle whose area is equal to the area of a circle of radius 7 cm ?

A plate on square base made of brass is of length x cm and width 1 mm. The plate weights 4725 gm. If 1 cubic cm cm of brass weight 8.4 grams, then the value of x is :

If the radius of a circle is increased by 75%, then its circumference will increase by :

The area of the largest circle, that can be drawn inside a rectangle with side 18 cm by 14 cm, is :

The area of a grassy plot is 480 sq. m. If each side had been 5 m longer, the area would have been increased by 245 sq. m. Find the length of the fence to surround it.

The perimeter of a rectangular field is 480 metres and the ratio between the length and the breadth is 5 : 3. The area is :

The perimeter of a square and a regular hexagon are equal. The ratio of the area of the hexagon to the area of the square is :

The ratio of circumference and diameter of a circle is 22 : 7. If the circumference be $$1\frac{4}{7}$$ m, then the radius of the circle is :

If the circumference of a circle is increased by 20%, what will be the effect on the circle ?

A circle is circumscribed around a square as shown in the figure. The area of one of the four shaded portions is equal to $$\frac{4}{7}$$. The radius of the circle is :

The area of a circle is increased by 22 sq. cm if its radius is increased by 1 cm. The original radius of the circle is :

Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is :

A circular pond has area equal to 616 m2. A circular stage is made at the centre of the pond whose radius is equal to half the radius of the pond. What is the area where water is present ?

ABCD is a rectangle and E and F are the mid-points of AD and DC respectively. Then the ratio of the areas of EDF and AEFC would be :

A rectangular farm has to be fenced on one long side, one short side and the diagonal. If the cost of fencing is Rs. 100 per m, the area of the farm is 1200 m2 and the short side is 30 m long, how much would the job cost ?

A hall 50 m long and 45 m broad is to be paved with square tiles. Find the largest tile as well as its number in the given options so that the tiles exactly fit in the hall :

If an equilateral triangle of area X and a square of area Y have the same perimeter, then X is :

In a triangle ABC, a line XY is drawn parallel to BC meeting AB in X and AC in Y. The area of the triangle AXY is half of the area of the triangle ABC. XY divides AB in the ratio of :

A hall, whose length is 16 m and the breadth is twice its height, takes 168 m of paper with 2 m as its width to cover its four walls. The area of the floor is :

If the sides of a square be double find the increase of percentage in area :

Three plots having areas 110, 130 and 190 square metres are to be subdivided into flower beds of equal size. If the breadth of a bed is 2 metres, the maximum length of a bed van be :

A rectangular lawn 80 metres by 60 metres has two roads each 10 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at Rs. 30 per square metre.

The length of a rectangular blackboard is 8 m more than its breadth. If its length is increased by 7 m and its breadth is decreased by 4 m, its area remains unchanged. The length and breadth of the rectangular blackboard is :