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Aptitude Round Question-Area-Free Download

Aptitude Round Question-Area-Free Download

Areas Formulae

1. Area of a rectangle = (Length x Breadth).
2. Length = Area/Breadth and Breadth = Area/Length
3. Perimeter of a rectangle = 2(Length + Breadth)
4. Area of a square = (side)2 = 1/2(diagonal)2.
5. Area of 4 walls of a room = 2 (Length + Breadth) x Height
6. Area of a triangle = 1/2x Base x Height.
7. Area of parallelogram = (Base x Height).
8. Area of a rhombus = 1/2x (Product of diagonals).
9. Area of a trapezium = 1/2x (sum of parallel sides) x distance between them.

1. What is the area of an equilateral triangle of side 16cm ?
a) 243 cm2
b) 64 3 cm2
c) 363 cm2
d)323 cm2

2. Consider the following figure. <A=x+30; <D= x-40. Find <B?
a. 125o
b. 55o
c. 155o
d. 122o

3. Find the area of a square, the product of whose diagonals is 66 cm2
a) 30 cm2
b) 33 cm2
c) 36 cm2
d) 42 cm2

4. A 5 cubic centimeter cube is painted on all its side. If it is sliced into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
a) 9
b) 61
c) 98
d) 54

5. Find the area of a trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
a) 225 cm2
b)275 cm2
c) 285 cm2
d)315 cm2

6. Examine the figure. <ADB=25o; Find <OBC:
a. 115o
b. 25o
c. 50o
d. 65o

7. The sector of a circle has radius of 21 cm and central angle 1350. Find its perimeter.
a) 91.5 cm
b)93.5 cm
c) 94.5 cm
d) 92.5 cm

8. The volumes of two cones are in the ratio of 1 :10 and the radii of the cones are in the ratio of 1 : 2, what is the ratio of their vertical heights?
a) 2 : 5
b) 1 : 5
c) 3 : 5
4) 4 : 5


Answer Key

1.c; 2.b; 3.b; 4.d; 5.c; 6.a; 7.a; 8.a

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

A.

15360

B.

153600

C.

30720

D.

307200

Answer: Option B

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

A.

2%

B.

2.02%

C.

4%

D.

4.04%

Answer: Option D

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A.

16 cm

B.

18 cm

C.

24 cm

D.

Data inadequate

E.

None of these

Answer: Option B

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

A.

40%

B.

42%

C.

44%

D.

46%

Answer: Option C


A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A.

2.91 m

B.

3 m

C.

5.82 m

D.

None of these

Answer: Option B

The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?

A.

5

1

4

B.

13

1

2

C.

27

D.

37

Answer: Option C


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.

10%

B.

10.08%

C.

20%

D.

28%

Answer: Option D

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

A.

20

B.

24

C.

30

D.

33

Answer: Option C

The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

A.

9 cm

B.

18 cm

C.

20 cm

D.

41 cm

Answer: Option B


What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

A.

814

B.

820

C.

840

D.

844

Answer: Option A


The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

A.

1520 m2

B.

2420 m2

C.

2480 m2

D.

2520 m2

Answer: Option D


The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

A.

25% increase

B.

50% increase

C.

50% decrease

D.

75% decrease

Answer: Option B

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

A.

40

B.

50

C.

120

D.

Data inadequate

E.

None of these

Answer: Option E


A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

A.

34

B.

40

C.

68

D.

88

Answer: Option D

A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

A.

Rs. 456

B.

Rs. 458

C.

Rs. 558

D.

Rs. 568

Answer: Option C

The area of a triangle is with base 4m and height 5m?

  • A. 20 sq m
  • B. 10 sq m
  • C. 5 sq m
  • D. 3 sq m

Answer: Option B

The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.

  • A. 0 sq m
  • B. 3 sq m
  • C. 2 sq m
  • D. 6 sq m

Answer: Option A

The length of each side of an equilateral triangle having an area of 4v3 cm 2 is?

Answer: Option D

1. The area of a triangle is with base 4m and height 5m?

  • A. 20 sq m
  • B. 10 sq m
  • C. 5 sq m
  • D. 3 sq m

Answer: Option B

The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.

  • A. 0 sq m
  • B. 3 sq m
  • C. 2 sq m
  • D. 6 sq m

Answer: Option A

The length of each side of an equilateral triangle having an area of 4v3 cm 2 is?

Answer: Option D

The altitude of an equilateral triangle of side 2v3 cm is?

Answer: Option D

The base of a right triangle is 8 and hypotenuse is 10. Its area is?

Answer: Option D

The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?

  • A. 3000 sq m
  • B. 3127 sq m
  • C. 3225 sq m
  • D. 3750 sq m

Answer: Option A

What is the area of square field whose side of length 15 m?

  • A. 225 sq m
  • B. 220 sq m
  • C. 100 sq m
  • D. 30 sq m

Answer: Option A

What is the area of a square field whose diagonal of length 20 m?

  • A. 300 sq m
  • B. 250 sq m
  • C. 200 sq m
  • D. 400 sq m

Answer: Option C

What is the perimeter of a square field whose diagonal is 8v2?

Answer: Option B

The ratio of the area of a square to that of the square drawn on its diagonal is?

Answer: Option D

11. The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?

  • A. 15v2 cm
  • B. 13v2 cm
  • C. 16v2 cm
  • D. 17v2 cm

Answer: Option B

If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?

Answer: Option C

A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?

  • A. 12 m, 10 m
  • B. 13 m, 12 m
  • C. 14 m, 11 m
  • D. 15 m, 10 m

swer: Option D

One side of a rectangular field is 4 m and its length along diagonal is 5 m. What is the area of the field?

  • A. 12 sq m
  • B. 4v14 sq m
  • C. 20 sq m
  • D. 15 sq m

nswer: Option A

A man walked 20 m to cross a rectangular field diagonally. If the length of the field is 16 cm. Find the breadth of the field is?

Answer: Option B

Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?

  • A. Rs.150
  • B. Rs.100
  • C. Rs.125
  • D. Rs.175

Answer: Option C

How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?

Answer: Option A

Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?

Answer: Option B

A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?

  • A. Rs.700
  • B. Rs.1200
  • C. Rs.1400
  • D. Rs.1500

Answer: Option B

The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?

Answer: Option B

The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?

  • A. Rs.1014
  • B. Rs.1140
  • C. Rs.999
  • D. Rs.1085

Answer: Option C

The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?

  • A. 432 sq m
  • B. 356 sq m
  • C. 452 sq m
  • D. 428 sq m

Answer: Option A

A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?

  • A. 675, Rs.1350
  • B. 575, Rs.1350
  • C. 1350, Rs.675
  • D. None

Answer: Option A

A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?

  • A. Rs.3600
  • B. Rs.3700
  • C. Rs.3800
  • D. Rs.3900

Answer: Option D

The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?

  • A. Remains same
  • B. 5% decrease
  • C. 5% increase
  • D. 10% increase

Answer: Option A

26. The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?

Answer: Option B

The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?

  • A. 529 sq m
  • B. 240 sq m
  • C. 260 sq m
  • D. 480 sq m

Answer: Option D

The diagonals of a rhombus are 15 cm and 20 cm. Find its area?

  • A. 120 sq m
  • B. 300 sq m
  • C. 150 sq m
  • D. 480 sq m

Option C

29. The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?

  • A. 260 cm2
  • B. 240 cm2
  • C. 280 cm2
  • D. 220 cm2

Answer: Option B

30. The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?

Answer: Option A

31. The side of a square is increased by 25% then how much % does its area increases?

Answer: Option B

The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?

Answer: Option D

33. The radius of a circle is increased by 1%. Find how much % does its area increases?

Answer: Option D

34. Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?

  • A. 120 sq m
  • B. 150 sq m
  • C. 110 sq m
  • D. 300 sq m

Answer: Option B

35. Find the area of circle whose radius is 7m?

  • A. 124 sq m
  • B. 154 sq m
  • C. 145 sq m
  • D. 167 sq m

Answer: Option B

6. If the area of circle is 616 sq cm then its circumference?

Answer: Option B

37. Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?

  • A. Rs.150
  • B. Rs.132
  • C. Rs.100
  • D. Rs.125

Answer: Option B

38. The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?

Answer: Option A

39. If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?

nswer: Option D

40. The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?

Answer: Option C

41. The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?

Answer: Option D

42. A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?

  • A. 1120 m2
  • B. 1250 m2
  • C. 1210 m2
  • D. 1200 m2

Answer: Option C

43. What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?

Answer: Option D

44. The radius of a semi circle is 6.3 cm then its perimeter is?

  • A. 35.4 cm
  • B. 32.4 cm
  • C. 32 cm
  • D. 30 cm

Answer: Option B

46. A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?

Answer: Option C

47. A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?

  • A. (400 - 100p) cm2
  • B. (400 - 2p) cm2
  • C. (400 Ė 200p) cm2
  • D. 200p cm2

Answer: Option A

48. The area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is?

  • A. 0.35 cm2
  • B. 17.5 cm2
  • C. 8.75 cm2
  • D. 55 cm2

Answer: Option C

49. The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42į is?

  • A. 26.4 m2
  • B. 39.6 m2
  • C. 52.8 m2
  • D. 79.2 m2

Answer: Option C

50. Which one of the following has a greater perimeter than the rest?

  • A. A square with an area of 36 sq.cm
  • B. An Equilateral Triangle with a side of 9 cm
  • C. A rectangle with 10 cm as length and 40 sq.cm as area
  • D. A circle with a radius of 4 cm

Answer: Option C

A big rectangular plot of area 4320 Sq.m is divided into 3 square shaped smaller plots by fencing parallel to the smaller side of the plot. However, some area of land was still left as a square plot could not be formed. So 3 more square shaped plots were formed by fencing parallel to the longer side of the original plot. Such that no area of the plot was left a surplus. What are the dimensions of the original plot?

  • A. 160m ◊ 27m
  • B. 240m ◊ 18m
  • C. 120m ◊ 36m
  • D. 135m ◊ 32m

Answer: Option C

In a Circle of Radius 5 cm if AB and AC are two equal chords of length 6cm each, then the length of chord BC is

  • 24/5 cm
  • B. 12/5 cm
  • C. 7/5 cm
  • D. None of these

Answer: Option D

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

  • A. 15.12 sq.cm
  • B. 13.52 sq.cm
  • C. 12.62 sq.cm
  • D. 10 sq.cm

Answer: Option B

The Length of a plot is four times is breadth. A playground measuring 1200 square meters occupies a third of the total area of the plot. What is the length of the plot in meters?

Answer: Option D

The length and breadth of play ground are 36 m and 21 m respectively. Flag staffs are required to be fixed on all along the boundary at a distance of 3 m part. The number of flag staffs will be:

Answer: Option B

The length and breadth of a rectangular piece of land are in the ratio of 5:3. The owner spent Rs 3000 for surroundings it from are the sides at Rs 7.50 per meter. The difference between is length and breadth is:

Answer: Option A

The ratio between the length and breadth of a rectangular field is 5:4. If the breadth is 20 meters less than the length. The perimeter of the field is:

  • A. 260m
  • B. 280m
  • C. 360m
  • D. None of these

Answer: Option C

60. If the side of a square is increased by 25 % then how much percent does itís area get increased:

Answer: Option D

61. The length of a hall is (4/3) times its breadth. If the area of the hall be 300 square meters the difference between the length and breadth is:

Answer: Option D

62. The area of a rectangle is thrice that of a square. The length of the rectangle is 40 cm and the breadth of the rectangle is (3/2) times of the square. The side of the square in cm is:

Answer: Option B

63. The length of a rectangle is increased by 60 %. By what percent would the width have to be decreased to maintain the same area?

Answer: Option A

64. If the ratio of the areas of two squares is 9:1 ratio of their perimeters is:

Answer: Option B

65. A hall 20 m long and 15 m broad is surrounded by a verandah of uniform width of 2.5 m. The cast of flooring the verandah at the rate of Rs 3.50 per sq. Meter is:

  • A. Rs.500
  • B. Rs. 600
  • C. Rs. 700
  • D. Rs. 800

Answer: Option C

66. 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:

Answer: Option C

67. The length of a rectangular room is 4 meters. If it can be partitioned into two equal square rooms. What is the length of each partition in meters:

Answer: Option B

68. A rectangle has 15 cm as its length and 159 cm^2 as its area. Its area is increased to 1 1/3 times the original area by increasing only its length its new perimeter is:

Answer: Option B

The length of a rectangle is twice its breadth, if length is decreased by 5 cm and the breadth is increased by 5 cm. The length of the rectangle is:

Answer: Option C

If the base of rectangle is increased by 10 % and the area is unchanged then the corresponding altitude must be decreased by:

Answer: Option A

71. If the diagonal of a square is doubled. How does the area of the square change?

  • A. Becomes fourfold
  • B. Becomes threefold
  • C. Becomes twofold
  • D. none of the above

Answer: Option A

73. Area of a square with side x is equal to the area of a triangle with base x. The altitude of the triangle is:

Answer: Option C

74. If the circumference of a circle is 352 meters then its area in Sq.m is:

Answer: Option A

75. If the radius of a circle be reduced by 50% its area is reduced by:

Answer: Option C

76. If the diameter of a circle is increased by 100 % its area is increased by:

Answer: Option C

77. A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ration of 6:5 The smaller side if the rectangle is:

Answer: Option B

78. The number of rounds that a wheel of diameter 7/11 m will make in going 4 km is:

Answer: Option D

The diameter of a circle is 105 cm less than the circumference what is the diameter of the circle?

Answer: Option D

81. The circumferences of two concentric circles are 176 m and 132 cm respectively. What is the difference between their radii?

Answer: Option B

82. The length of a rope by which a cow must be tethered in order that she may be able to graze an area of 9856 sq.m is:

Answer: Option A

83. In a rhombus whose area is 144 sq.cm on of its diagonals is twice as long as the other. The lengths of its diagonals are:

  • A. 24 cm,48cm
  • B. 12cm,24cm
  • C. 6v2cm,12v2cm
  • D. 6cm,12cm

Answer: Option B

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

  • A. greater than 1
  • B. equal to 1
  • C. equal to 1/2
  • D. equal to ľ

Answer: Option B

85. A parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long then its area is:

  • A. 480 sq.m
  • B. 320 sq.m
  • C. 600v15 sq.m
  • D. 450v15

Answer: Option C

86. A rectangular carpet has an area of 120 sq.m and a perimeter of 46 m. The length of its diagonal is:

Answer: Option C

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

Answer: Option B

88. The length of a rectangular plot is 4 Ĺ times that of its breadth. IF the area of the plot is 200 square meters, then what is itís length?

Answer: Option E

89. The Ratio of the length and breadth of a plot is 3:2 .If the breadth is 40m less than the what is the parameter of the plot?

Answer: Option C

90. A rectangular carpet has an area of 120 square meters and a parameter of 46m. The length of itís diagonals is

Answer: Option D

91. A room is 12 ľ m long and 7w wide. The maximum length of a square tile to fill the floor of the room with whole number of itís tiles should be

Answer: Option B

92. A rectangular courtyard 3.78min long and 5.25m broad is to be paved exactly with square tiles all of the same size. The minimum number of such tiles is

Answer: Option C

93. The perimeter of a floor of a room is 18m.What is the area of four walls of the room if it; a height is 3m?

  • A. 21 Sq.m
  • B. 42 Sq.m
  • C. 54 Sq.m
  • D. 108 Sq.m

Answer: Option C

94. A rectangular measure 8cm on length and itís diagonals measures 10cm what is the perimeter of the rectangular?

Answer: Option C

95. How many meters of carpet 63cm will be required to be a floor of a room 14m by 9cm?

Answer: Option A

96. A path of uniform width turns the inside of a rectangular field 38m long and 32m wide. IF the path occupies 600 m2 than the width of the path is

Answer: Option B

97. Total area of the 64 small squares of aches board is 400cm2. There is 3cm wide border around the chess board. What is the length of each side of the chess board?

Answer: Option D

98. The length of a rectangular increased by 10% and it;s breadth is decreased by 10 %. Then the area of the new rectangle is

  • A. Neither increased nor decreased
  • B. Increased by 1%
  • C. Decreased by 1%
  • D. Decreased by 10%

Answer: Option C

99. If the diagonal of a rectangle is 17cm long and perimeter is 46 cm the area of the rectangle is

  • A. 100cm2
  • B. 110cm2
  • C. 120cm2
  • D. 150cm2

Answer: Option C

100. The Total cost of flooring a room at Rs.8.50 per square meter is Rs.510. If the length of the room is 8km itís breadth is

Answer: Option A

101. A rectangular field has dimensions 25m by 15m. Two mutually perpendicular passage of 2m width have been left in itís central part and grass has been grown in rest of the field. The area under the grass is:

Answer: Option B

102. The perimeter of a rectangle is 60m. If itís length is twice its breadth then its area is

Answer: Option C

103. The area of a rectangle is 12 sq.metres and itís length is 3 times that of itís breadth. What is the perimeter of the rectangle

Answer: Option D

104. The largest size of bamboo that can be placed in a square of area 100 sq.meters is:

Answer: Option B

105. The diagonal of a square is 4v2cm. The diagonal is another square whose area is double that of the first square is

Answer: Option A

106. The perimeter of a rectangle and square are 160m each. The area of the rectangle is less than that itís square by 100cm meters. The less than that of the square by 100 sq.meters. the length of rectangle is

Answer: Option C

107. The length of a rectangular plot is twice its breadth. If the area of the rectangular plot is 6075 sq.meters .what is its length?

  • A. 45m
  • B. 75m
  • C. 130m
  • D. None of these

Answer: Option D

108. The length of a rectangular plot is increased by 25%. To keep itís area uncharged the width of the plot should be

  • A. Kept unchanged
  • B. Increased by 25%
  • C. Increased by 20%
  • D. Reduced by 20%

Answer: Option D

109. If the length and width of a rectangular grand are each increased by 20% then what would be the percent increase in the area of the garden?

Answer: Option D

110. If the length of a rectangle is increased by 20% and itís breadth is decreased by 20% then it area

  • A. Increased by 4%
  • B. decreased by 4%
  • C. Decreased by 1%
  • D. Remains unchanged

Answer: Option B

.

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