30 Area

 EXERCISE 24A

(OBJECTIVE TYPE QUESTIONS)

Directions : Mark (✓) against the correct answer :

1. The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 800 per sq. metre. (IGNOU, 2003)

(a) Rs. 15,000

(b) Rs. 15,550

(c) Rs. 15,600

(d) Rs. 16,500

2. The length of a rectangle is 18 cm and its breadth is 10 cm. When the length is increased to 25 cm, what will be the breadth of the rectangle if the area remains the same ?

(a) 7 cm

(b) 7.1 cm

(c) 7.2 cm

(d) 7.3 cm

3. A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed ?

(a) 55

(b) 56

(c) 57

(d) 58

4. The length of a rectangular plot is 60% more than its breadth. If the difference between the length and the breadth of that rectangle is 24 cm, what is the area of that rectangle ? (Bank P.O. 1998)

(a) 2400 sq. cm

(b) 2480 sq. cm

(c) 2560 sq. cm

(d) Data inadequate

(e) None of these

5. A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet ? (M.A.T. 2003)

(a) 46

(b) 81

(c) 126

(d) 252

6. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is : (Section Officers', 2003)

(a) 1520 m²

(b) 2420 m²

(c) 2480 m²

(d) 2520 m²

7. The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres ? (Bank P.O. 1999)

(a) 40

(b) 50

(c) 120

(d) Data inadequate

(e) None of these

8. The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m, what is the area of the field ?

(a) 18750 sq. m

(b) 37500 sq. m

(c) 40000 sq. m

(d) 48000 sq. m

9. The ratio between the length and the perimeter of a rectangular plot is 1 : 3. What is the ratio between the length and breadth of the plot ?

(a) 1 : 2

(b) 2 : 1

(c) 3 : 2

(d) Data inadequate

10. 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 : (S.S.C. 2003)

(a) 15360

(b) 153600

(c) 30720

(d) 307200

11. The length of a rectangular hall is 5 m more than its breadth. The area of the hall is 750 m². The length of the hall is : (S.S.C. 2004)

(a) 15 m

(b) 22.5 m

(c) 25 m

(d) 30 m

12. The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field ? (Bank P.O. 2003)

(a) 15 metres

(b) 26 metres

(c) 34.5 metres

(d) Cannot be determined

(e) None of these

18. 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

(R.R.B. 2002)

14. 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

(B.S.R.B. 1998)

15. 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) 15 m × 6.67 m

(b) 20 m × 5 m

(c) 30 m × 3.33 m

(d) 40 m × 2.5 m

(R.R.B. 2003)

16. The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 7500 sq. m, the cost of fencing the field @ 25 paise per metre is :

(a) Rs. 55.50

(b) Rs. 67.50

(c) Rs. 86.50

(d) Rs. 87.50

17. A rectangle of certain dimensions is chopped off from one corner of a larger rectangle as shown. AB = 8 cm and BC = 4 cm. The perimeter of the figure ABCPQRA (in cm) is :

(Asstt. Grade, 1998)

(a) 24

(b) 28

(c) 36

(d) 48

18. A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares ?

(a) 225

(b) 280

(c) 300

(d) 315

19. 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 ?

(S.S.C. 2000)

(a) 140 cm²

(b) 240 cm²

(c) 560 cm²

(d) None of these

20. A rectangular plot is half as long again as it is broad and its area is $\frac{2}{3}$ hectares. Then, its length is :

(a) 100 m

(b) 33.33 m

(c) 66.66 m

(d) $\frac{100\sqrt{3}}{3}$ m

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

(a) 18000

(b) 20000

(c) 25000

(d) None of these

22. The cost of carpeting a room 18 m long with a carpet 75 cm wide at Rs. 4.50 per metre is Rs. 810. The breadth of the room is :

(a) 7 m

(b) 7.5 m

(c) 8 m

(d) 8.5 m

23. The diagonal of the floor of a rectangular closet is $\frac{1}{2}$ feet. The shorter side of the closet is $4\frac{1}{2}$ feet. What is the area of the closet in square feet ?

(M.B.A. 2003)

(a) $5\frac{1}{4}$

(b) $12\frac{1}{2}$

(c) 27

(d) 37

24. The length of a rectangle is three times of its width. If the length of the diagonal is 8√10 cm, then the perimeter of the rectangle is : (S.S.C. 2000)

(a) 15√10 cm

(b) 16√10 cm

(c) 24√10 cm

(d) 64 cm

25. The diagonal of a rectangle is thrice its smaller side. The ratio of the length to the breadth of the rectangle is :

(a) 3 : 1

(b) √3 : 1

(c) √2 : 1

(d) 2√2 : 1

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

(a) 15 m

(b) 16 m

(c) 17 m

(d) 20 m

27. The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be : (Hotel Management, 2002)

(a) 9 cm

(b) 18 cm

(c) 20 cm

(d) 41 cm

28. A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68 m/min. The area of the field is : (S.S.C. 2003)

(a) 30 m²

(b) 40 m²

(c) 50 m²

(d) 60 m²

29. 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) 5 m

(b) 12 m

(c) 13 m

(d) 14.5 m

30. The ratio between the length and the breadth of a rectangular field is 3 : 2. If only the length is increased by 5 metres, the new area of the field will be 2600 sq. metres. What is the breadth of the rectangular field ?

(a) 40 metres

(b) 60 metres

(c) 65 metres

(d) Cannot be determined

(e) None of these

31. The length of a blackboard is 8 cm more than its breadth. If the length is increased by 7 cm and breadth is decreased by 4 cm, the area remains the same. The length and breadth of the blackboard (in cm) will be :

(a) 28, 20

(b) 34, 26

(c) 40, 32

(d) 56, 48

32. If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq. m. If the length is increased by 1 m and breadth is decreased by 1 m, then the area is decreased by 5 sq. m. The perimeter of the floor is :

(a) 30 m

(b) 32 m

(c) 36 m

(d) 40 m

33. The percentage increase in the area of a rectangle, if each of its sides is increased by 20%, is : (M.A.T. 2004)

(a) 40%

(b) 42%

(c) 44%

(d) 46%

34. A rectangle has width a and length b. If the width is decreased by 20% and the length is increased by 10%, then what is the area of the new rectangle in percentage compared to 'ab' ? (R.R.B. 2002)

(a) 80%

(b) 88%

(c) 110%

(d) 120%

35. If the length and breadth of a rectangular plot be increased by 50% and 20% respectively, then how many times will its area be increased ? (Bank P.O. 2003)

(a) 1 1/3

(b) 2

(c) 3 2/5

(d) 4 1/5

(e) None of these

36. 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 : (N.I.F.T. 1997)

(a) 10%

(b) 10.08%

(c) 20%

(d) 28%

Area

509

37. The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area ? (S.S.C. 2000)

(a) 25% increase

(b) 50% increase

(c) 50% decrease

(d) 75% decrease

38. The length of a rectangle is decreased by r%, and the breadth is increased by (r + 5)%. Find r, if the area of the rectangle is unaltered. (SCMHRD, 2002)

(a) 5

(b) 8

(c) 10

(d) 15

(e) 20

39. The length of a rectangle is increased by 60%. By what percent would the width have to be decreased so as to maintain the same area ? (M.A.T. 2003)

(a) 37 1/2%

(b) 60%

(c) 75%

(d) 120%

40. If the area of a rectangular plot increases by 30% while its breadth remains same, what will be the ratio of the areas of new and old figures ? (Bank P.O. 2003)

(a) 1 : 3

(b) 3 : 1

(c) 4 : 7

(d) 10 : 13

(e) None of these

41. A typist uses a sheet measuring 20 cm by 30 cm lengthwise. If a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then percent of the page used for typing is : (M.A.T. 1998)

(a) 40

(b) 60

(c) 64

(d) 72

42. A room is 15 feet long and 12 feet broad. A mat has to be placed on the floor of this room leaving 1 1/2 feet space from the walls. What will be the cost of the mat at the rate of Rs. 3.50 per square feet ? (R.R.B. 2002)

(a) Rs. 378

(b) Rs. 472.50

(c) Rs. 496

(d) Rs. 630

43. What will be the cost of gardening 1 metre broad boundary around a rectangular plot having perimeter of 340 metres at the rate of Rs. 10 per square metre ? (a) Rs. 1700 (b) Rs. 3400 (c) Rs. 3440 (d) Cannot be determined (e) None of these (Bank P.O. 2003)
44. 2 metres broad pathway is to be constructed around a rectangular plot on the inside. The area of the plot is 96 sq. m. The rate of construction is Rs. 50 per square metre. Find the total cost of the construction. (S.B.I.P.O. 2000)

(a) Rs. 2400

(b) Rs. 4000

(c) Rs. 4800

(d) Data inadequate

(e) None of these

45. Within a rectangular garden 10 m wide and 20 m long, we wish to pave a walk around the borders of uniform width so as to leave an area of 96 m² for flowers. How wide should the walk be ? (a) 1 m (b) 2 m (c) 2.1 m (d) 2.5 m
46. A rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. The cost of gravelling the roads at 75 paise per sq. metre is : (a) Rs. 254.50 (b) Rs. 258 (c) Rs. 262.50 (d) Rs. 270
47. 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 ? (M.A.T. 1997)

(a) 2.91 m

(b) 3 m

(c) 5.82 m

(d) None of these

48. A housing society has been allotted a square piece of land measuring 2550.25 sq. m. What is the side of the plot ? (a) 50.25 m (b) 50.5 m (c) 50.65 m (d) None of these
49. The cost of cultivating a square field at the rate of Rs. 135 per hectare is Rs. 1215. The cost of putting a fence around it at the rate of 75 paise per metre would be : (a) Rs. 360 (b) Rs. 810 (c) Rs. 900 (d) Rs. 1800
50. The perimeters of five squares are 24 cm, 32 cm, 40 cm, 76 cm and 80 cm respectively. The perimeter of another square equal in area to the sum of the areas of these squares is : (S.S.C. 2004) (a) 31 cm (b) 62 cm (c) 124 cm (d) 961 cm
51. The number of marble slabs of size 20 cm × 30 cm required to pave the floor of a square room of side 3 metres, is : (a) 100 (b) 150 (c) 225 (d) 250
52. 50 square stone slabs of equal size were needed to cover a floor area of 72 sq. m. The length of each stone slab is : (S.S.C. 2003) (a) 102 cm (b) 120 cm (c) 201 cm (d) 210 cm
53. 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) 16 (b) 24 (c) 32 (d) 48 (e) None of these (S.B.I.P.O. 2000)
54. What is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m : cm broad ? (S.S.C. 2003) (a) 814 (b) 820 (c) 840 (d) 844
55. A rectangular room can be partitioned into two equal square rooms by a partition 7 metres long. What is the area of the rectangular room in square metres ? (a) 49 (b) 147 (c) 196 (d) None of these
56. The perimeter of a square is 48 cm. The area of a rectangle is 4 cm² less than the area of the square. If the length of the rectangle is 14 cm, then its perimeter is : (a) 24 cm (b) 48 cm (c) 50 cm (d) 54 cm (S.S.C. 2002)
57. 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 of the square, then the side of the square is : (a) 15 cm (b) 20 cm (c) 30 cm (d) 60 cm
58. If the perimeter of a rectangle and a square, each is equal to 80 cm and the difference of their areas is 100 sq. cm, the sides of the rectangle are : (a) 25 cm, 15 cm (b) 28 cm, 12 cm (c) 30 cm, 10 cm (d) 35 cm, 15 cm
59. The cost of fencing a square field @ Rs. 20 per metre is Rs. 10,080. How much will it cost to lay a three metre wide pavement along the fencing inside the field @ Rs. 50 per sq. metre ? (a) Rs. 37,350 (b) Rs. 73,800 (c) Rs. 77,400 (d) None of these
60. A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1784 square metres. What is the perimeter along the outer edge of the road ? (Bank P.O. 1998) (a) 576 metres (b) 600 metres (c) 640 metres (d) Data inadequate (e) None of these
61. A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges ? (M.B.A. 2003) (a) 20 (b) 24 (c) 30 (d) 33
62. A man walking at the speed of 4 kmph crosses a square field diagonally in 3 minutes. The area of the field is : (a) 18000 m² (b) 19000 m² (c) 20000 m² (d) 25000 m²
63. 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

(R.R.B. 2003)

64. The area of a square field is 69696 cm². Its diagonal will be equal to :

(a) 313.296 m

(b) 353.296 m

(c) 373.296 m

(d) 393.296 m

(S.S.C. 1999)

65. What will be the length of the diagonal of that square plot whose area is equal to the area of a rectangular plot of length 45 metres and breadth 40 metres ?

(a) 42.5 metres

(b) 60 metres

(c) 75 metres

(d) Data inadequate

(e) None of these

(Bank P.O. 1999)

66. The length of a rectangle is 20% more than its breadth. What will be the ratio of the area of a rectangle to that of a square whose side is equal to the breadth of the rectangle ?

(a) 2 : 1

(b) 5 : 6

(c) 6 : 5

(d) Data inadequate

(e) None of these

(Bank P.O. 2000)

67. A square and a rectangle have equal areas. If their perimeters are $p_1$ and $p_2$ respectively, then :

(a) $p_1 < p_2$

(b) $p_1 = p_2$

(c) $p_1 > p_2$

(d) None of these

68. If the perimeters of a square and a rectangle are the same, then the area A and B enclosed by them would satisfy the condition :

(a) A < B

(b) A ≤ B

(c) A > B

(d) A ≥ B

69. The diagonal of a square is $4\sqrt{2}$ cm. The diagonal of another square whose area is double that of the first square, is :

(a) 8 cm

(b) $8\sqrt{2}$ cm

(c) $4\sqrt{2}$ cm

(d) 16 cm

(S.S.C. 2002)

70. The ratio of the area of a square to that of the square drawn on its diagonal, is :

(a) 1 : 2

(b) 2 : 3

(c) 3 : 4

(d) 4 : 5

(GNDU, 2003)

71. The ratio of the areas of two squares, one having its diagonal double than the other, is :

(a) 2 : 1

(b) 2 : 3

(c) 3 : 1

(d) 4 : 1

72. If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is :

(a) 225 : 256

(b) 256 : 225

(c) 15 : 16

(d) 16 : 15

(S.S.C. 2004)

73. 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) 100 m²

(b) 101 m²

(c) 200 m²

(d) 201 m²

74. If each side of a square is increased by 50%, the ratio of the area of the resulting square to that of the given square is :

(a) 4 : 5

(b) 5 : 4

(c) 4 : 9

(d) 9 : 4

75. What happens to the area of a square when its side is halved ? Its area will :

(a) remain same

(b) become half

(c) become one-fourth

(d) become double

(R.R.B. 2003)

76. An error of 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%

(C.D.S. 2003)

77. If the area of a square increases by 69%, then the side of the square increases by :

(a) 13%

(b) 30%

(c) 39%

(d) 69%

(M.A.T. 1998)

78. If the diagonal of a square is made 1.5 times, then the ratio of the areas of two squares is :

(a) 4 : 3

(b) 4 : 5

(c) 4 : 7

(d) 4 : 9

79. 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) 35%

(b) 42%

(c) 62%

(d) 82%

80. The length of one pair of opposite sides of a square is increased by 5 cm on each side; the ratio of the length and the breadth of the newly formed rectangle becomes 3 : 2. What is the area of the original square ?

(Bank P.O. 1999)

(a) 25 sq. cm

(b) 81 sq. cm

(c) 100 sq. cm

(d) 225 sq. cm

(e) None of these

81. If the side of a square is increased by 5 cm, the area increases by 165 sq. cm. The side of the square is :

(a) 12 cm

(b) 13 cm

(c) 14 cm

(d) 15 cm

82. The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm.

(S.S.C. 2003)

(a) 7 cm

(b) 9 cm

(c) 11 cm

(d) 16 cm

83. 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.

(S.S.C. 2002)

(a) 17 cm

(b) 26 cm

(c) 30 cm

(d) 34 cm

84. 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 :

(C.B.I. 1997)

(a) Rs. 456

(b) Rs. 458

(c) Rs. 558

(d) Rs. 568

85. The dimensions of a room are 10 m × 7 m × 5 m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1 m × 3 m. One window is of size 2 m × 1.5 m and the other two windows are of size 1 m × 1.5 m. The cost of painting the walls at Rs. 3 per m² is :

(a) Rs. 474

(b) Rs. 578.50

(c) Rs. 684

(d) Rs. 894

86. The cost of papering the four walls of a room is Rs. 475. Each one of the length, breadth and height of another room is double that of this room. The cost of papering the walls of this new room is :

(a) Rs. 712.50

(b) Rs. 950

(c) Rs. 1425

(d) Rs. 1900

87. The ratio of height of a room to its semi-perimeter is 2 : 5. It costs Rs. 260 to paper the walls of the room with paper 50 cm wide at Rs. 2 per metre allowing an area of 15 sq. m for doors and windows. The height of the room is :

(a) 2.6 m

(b) 3.9 m

(c) 4 m

(d) 4.2 m

88. The base of a triangle is 15 cm and height is 12 cm. The height of another triangle of double the area having the base 20 cm is :

(S.S.C. 2002)

(a) 8 cm

(b) 9 cm

(c) 12.5 cm

(d) 18 cm

89. ABC is a triangle with base AB. D is a point on AB such that AB = 5 and DB = 3. What is the ratio of the area of △ADC to the area of △ABC ?

(S.S.C. 2000)

(a) 2 : 3

(b) 3 : 2

(c) 2 : 5

(d) 3 : 5

90. The area of a right-angled triangle is 40 times its base. What is its height ?

(a) 45 cm

(b) 60 cm

(c) 80 cm

(d) Data inadequate

(e) None of these

(B.S.B.B. 1998)

91. If the area of a triangle is 1176 cm² and base : corresponding altitude is 3 : 4, then the altitude of the triangle is :

(S.S.C. 2000)

(a) 42 cm

(b) 52 cm

(c) 54 cm

(d) 56 cm

92. The three sides of a triangle are 5 cm, 12 cm and 13 cm respectively. Then, its area is :

(a) $10\sqrt{3}$ cm²

(b) $10\sqrt{6}$ cm²

(c) 20 cm²

(d) 30 cm²

93. The sides of a triangle are in the 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 :

(M.A.T. 2004)

(a) 9 cm

(b) 10 cm

(c) 11 cm

(d) 12 cm

94. The area of a triangle is 216 cm² and its sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is :

(S.S.C. 2004)

(a) 6 cm

(b) 12 cm

(c) 36 cm

(d) 72 cm

95. The sides of a triangle are 3 cm, 4 cm and 5 cm. The area (in cm²) of the triangle formed by joining the mid-points of the sides of this triangle is :

(S.S.C. 2003)

(a) $\frac{3}{4}$

(b) $\frac{3}{2}$

(c) 3

(d) 6

96. One side of a right-angled triangle is twice the other, and the hypotenuse is 10 cm. The area of the triangle is :

(a) 20 cm²

(b) $33\frac{1}{3}$ cm²

(c) 40 cm²

(d) 50 cm²

97. The perimeter of a right-angled triangle is 60 cm. Its hypotenuse is 26 cm. The area of the triangle is :

(M.B.A. 2002)

(a) 120 cm²

(b) 240 cm²

(c) 390 cm²

(d) 780 cm²

98. If the perimeter of an isosceles right triangle is $(6 + 3\sqrt{2})$ m, then the area of the triangle is :

(M.A.T. 2003)

(a) 4.5 m²

(b) 5.4 m²

(c) 9 m²

(d) 81 m²

99. The perimeter of a triangle is 30 cm and its area is 30 cm². If the largest side measures 13 cm, then what is the length of the smallest side of the triangle ?

(a) 3 cm

(b) 4 cm

(c) 5 cm

(d) 6 cm

(S.S.C. 2003)

100. If the area of an equilateral triangle is $24\sqrt{3}$ sq. cm, then its perimeter is :

(a) $2\sqrt{6}$ cm

(b) $4\sqrt{6}$ cm

(c) $12\sqrt{6}$ cm

(d) 96 cm

101. The height of an equilateral triangle is 10 cm. Its area is :

(S.S.C. 2003)

(a) $\frac{100}{3}$ cm²

(b) 30 cm²

(c) 100 cm²

(d) $\frac{100}{\sqrt{3}}$ cm²

102. From a point in the interior of an equilateral triangle, the perpendicular distance of the sides are $\sqrt{3}$ cm, $2\sqrt{3}$ cm and $5\sqrt{3}$ cm. The perimeter (in cm) of the triangle is :

(a) 24

(b) 32

(c) 48

(d) 64

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

(a) $x^2$

(b) $\frac{1}{2} x^2$

(c) $\frac{\sqrt{3}}{2} x^2$

(d) $\frac{\sqrt{3}}{3} x^2$

104. If the area of a square with side a is equal to the area of a triangle with base a, then the altitude of the triangle is :

(B.S.F. 2001)

(a) $\frac{a}{2}$

(b) a

(c) $2a$

(d) $4a$

105. An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square ?

(S.S.C. 2002)

(a) $2 : \sqrt{3}$

(b) $4 : \sqrt{3}$

(c) $\sqrt{3} : 2$

(d) $\sqrt{3} : 4$

106. What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?

(S.B.I.P.O. 1999)

(a) 1 : 2

(b) 2 : 1

(c) 3 : 1

(d) Data inadequate

(e) None of these

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

(C.D.S. 2003)

(a) equal to Y

(b) greater than Y

(c) less than Y

(d) less than or equal to Y

108. A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12√2 cm, then the area of the triangle is :

(a) 24√2 cm²

(b) 24√3 cm²

(c) 48√3 cm²

(d) 64√3 cm²

109. 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 :

(S.S.C. 2004)

(a) ax : by

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

(c) ay : bx

(d) $\frac{x}{a} : \frac{b}{y}$

110. If the side of an equilateral triangle is decreased by 20%, its area is decreased by :

(a) 36%

(b) 40%

(c) 60%

(d) 64%

(C.B.I. 1997)

111. 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 ?

(S.B.I.P.O. 2000)

(a) No change

(b) 8% decrease

(c) 16% decrease

(d) 16% increase

(e) None of these

112. If every side of a triangle is doubled, the area of the new triangle is K times the area of the old one. K is equal to :

(R.R.B. 2003)

(a) √2

(b) 2

(c) 3

(d) 4

113. One side of a parallelogram is 18 cm and its distance from the opposite side is 8 cm. The area of the parallelogram is :

(a) 48 cm²

(b) 72 cm²

(c) 100 cm²

(d) 144 cm²

114. A parallelogram has sides 30 m and 14 m and one of its diagonals is 40 m long. Then, its area is :

(a) 158 m²

(b) 336 m²

(c) 372 m²

(d) 480 m²

115. One diagonal of a parallelogram is 70 cm and the perpendicular distance of this diagonal from either of the outlying vertices is 27 cm. The area of the parallelogram (in sq. cm) is :

(a) 1800

(b) 1836

(c) 1890

(d) 1980

116. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is :

(M.A.T. 2003)

(a) 10√2 m

(b) 100 m

(c) 100√2 m

(d) 200 m

117. If a parallelogram with area P, a rectangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then which of the following statements is false ?

(a) P = R

(b) P + T = 2R

(c) P = 2T

(d) T = (1/2) R

118. The area of a rhombus is 150 cm². The length of one of its diagonals is 10 cm. The length of the other diagonal is :

(S.S.C. 2004)

(a) 25 cm

(b) 30 cm

(c) 35 cm

(d) 40 cm

119. One of the diagonals of a rhombus is double the other diagonal. Its area is 25 sq. cm. The sum of the diagonals is : (S.S.C. 2003) (a) 10 cm (b) 12 cm (c) 15 cm (d) 16 cm
120. The perimeter of a rhombus is 56 m and its height is 5 m. Its area is : (a) 64 sq. m (b) 70 sq. m (c) 78 sq. m (d) 84 sq. m
121. If the diagonals of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus are respectively : (a) 120 cm², 52 cm (b) 120 cm², 64 cm (c) 240 cm², 52 cm (d) 240 cm², 64 cm
122. Each side of a rhombus is 26 cm and one of its diagonals is 48 cm long. The area of the rhombus is : (R.R.B. 2003) (a) 240 cm² (b) 300 cm² (c) 360 cm² (d) 480 cm²
123. The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of the other diagonal ? (a) 4/5 (b) 2/5 (c) 2/4 (d) 1/4
124. 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) greater than 1 (b) equal to 1 (c) equal to 1/2 (d) equal to 1/4
125. The 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 : (a) 10 m² (b) 13 m² (c) 20 m² (d) 26 m²
126. The area of a field in the shape of a trapezium measures 1440 m². The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is 5 : 3, the length of the longer parallel side is : (S.S.C. 2004) (a) 45 m (b) 60 m (c) 75 m (d) 120 m
127. The 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 sq. m, the depth of the canal is : (a) 8.75 m (b) 42 m (c) 63 m (d) 84 m
128. The area of a circle of radius 5 is numerically what percent of its circumference ? (a) 200 (b) 225 (c) 240 (d) 250 (S.S.C. 2000)
129. A man runs round a circular field of radius 50 m at the speed of 12 km/h. What is the time taken by the man to take twenty rounds of the field ? (M.A.T. 1997) (a) 30 min. (b) 32 min. (c) 34 min. (d) None of these
130. A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq. ft. per day, then approximately what time will be taken by the cow to graze the whole field ? (Bank P.O. 2003) (a) 2 days (b) 6 days (c) 18 days (d) 24 days (e) None of these
131. 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 ? (Bank P.O. 2004) (a) 88 cm² (b) 154 cm² (c) 1250 cm² (d) Cannot be determined (e) None of these
132. The circumference of a circle, whose area is 24.64 m², is : (R.R.B. 2003) (a) 14.64 m (b) 16.36 m (c) 17.60 m (d) 18.40 m
133. If the circumference and the area of a circle are numerically equal, then the diameter is equal to : (S.S.C. 2000) (a) 2/3 (b) 2/4 (c) 2 (d) 4
134. The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is : (Section Officers', 2001)

(a) 111 cm²

(b) 148 cm²

(c) 154 cm²

(d) 259 cm²

135. The sum of areas of two circles A and B is equal to the area of a third circle C whose diameter is 30 cm. If the diameter of circle A is 18 cm, then the radius of circle B is : (S.S.C. 2000)

(a) 10 cm

(b) 12 cm

(c) 15 cm

(d) 18 cm

136. Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has larger area and by how much ? (S.S.C. 2000)

(a) Both have equal area

(b) Square, 33 cm²

(c) Circle, 33 cm²

(d) Square, 495 cm²

137. A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its area will be : (R.R.B. 2002)

(a) 3520 cm²

(b) 6400 cm²

(c) 7744 cm²

(d) 8800 cm²

138. A wire when bent in the form of a square encloses an area of 484 sq. cm. What will be the enclosed area when the same wire is bent into the form of a circle ? (S.S.C. 2002)

(a) 462 sq. cm

(b) 539 sq. cm

(c) 616 sq. cm

(d) 693 sq. cm

139. A circular wire of radius 42 cm is bent in the form of a rectangle whose sides are in the ratio of 6 : 5. The smaller side of the rectangle is : (S.S.C. 2004)

(a) 25 cm

(b) 30 cm

(c) 36 cm

(d) 60 cm

140. There is a rectangular tank of length 180 m and breadth 120 m in a circular field. If the area of the land portion of the field is 40000 m², what is the radius of the field ? (IGNOU, 2003)

(a) 130 m

(b) 135 m

(c) 140 m

(d) 145 m

141. The areas of two circular fields are in the ratio 16 : 49. If the radius of the latter is 14 m, then what is the radius of the former ? (IGNOU, 2003)

(a) 4 m

(b) 8 m

(c) 18 m

(d) 32 m

142. If the ratio of areas of two circles is 4 : 9, then the ratio of their circumferences will be : (R.R.B. 2003)

(a) 2 : 3

(b) 3 : 2

(c) 4 : 9

(d) 9 : 4

143. The perimeter of a circle is equal to the perimeter of a square. Then, their areas are in the ratio : (S.S.C. 2003)

(a) 4 : 1

(b) 11 : 7

(c) 14 : 11

(d) 22 : 7

144. The diameter of a wheel is 1.26 m. How far will it travel in 500 revolutions ? (S.S.C. 2003)

(a) 1492 m

(b) 1980 m

(c) 2530 m

(d) 2880 m

145. The number of revolutions a wheel of diameter 40 cm makes in travelling a distance of 176 m, is : (S.S.C. 2003)

(a) 140

(b) 150

(c) 160

(d) 166

146. The radius of a wheel is 0.25 m. The number of revolutions it will make to travel a distance of 11 km will be : (R.R.B. 2003)

(a) 2800

(b) 4000

(c) 5500

(d) 7000

147. The wheel of an engine, 7 1/2 metres in circumference makes 7 revolutions in 9 seconds. The speed of the train in km per hour is : (S.S.C. 2003)

(a) 130

(b) 132

(c) 135

(d) 150

148. The wheel of a motorcycle, 70 cm in diameter, makes 40 revolutions in every 10 seconds. What is the speed of the motorcycle in km/hr ? (R.R.B. 2002)

(a) 22.32

(b) 27.68

(c) 31.68

(d) 36.24

149. 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 : (M.A.T. 2003)

(a) 22 cm/sec

(b) 44 cm/sec

(c) 66 cm/sec

(d) 122 cm/sec

150. A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions ? (a) 18

(b) 20

(c) 25

(d) 30

151. Find the diameter of a wheel that makes 113 revolutions to go 2 km 26 decametres.

(a) $4\frac{4}{13}$ m

(b) $6\frac{4}{11}$ m

(c) $12\frac{4}{11}$ m

(d) $12\frac{8}{11}$ m

(S.S.C. 2003)

152. The front wheels of a wagon are 2π feet in circumference and the rear wheels are 3π feet in circumference. When the front wheels have made 10 more revolutions than the rear wheels, how many feet has the wagon travelled ? (M.B.A. 2003)

(a) 30π

(b) 60π

(c) 90π

(d) 150π

153. A circular ground whose diameter is 35 metres, has a 1.4 m broad garden around it. What is the area of the garden in square metres ? (S.B.I.P.O. 1999)

(a) 160.16

(b) 176.16

(c) 196.16

(d) Data inadequate

(e) None of these

154. A circular garden has a circumference of 440 m. There is a 7 m wide border inside the garden along its periphery. The area of the border is : (a) 2918 m²

(b) 2921 m²

(c) 2924 m²

(d) 2926 m²

155. The areas of two concentric circles forming a ring are 154 sq. cm and 616 sq. cm. The breadth of the ring is : (a) 7 cm

(b) 14 cm

(c) 21 cm

(d) 28 cm

156. The ratio of the outer and the inner perimeters of a circular path is 23 : 22. If the path is 5 metres wide, the diameter of the inner circle is : (S.S.C. 2004)

(a) 55 m

(b) 110 m

(c) 220 m

(d) 230 m

157. 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 : (Assistant Grade, 1998)

(a) 8 ft

(b) 16 ft

(c) 20 ft

(d) 30 ft

158. The ratio of the outer and the inner circumferences of a circular path is 23 : 22. If the path is 5 m wide, the radius of the inner circle is :

(a) 55 m

(b) 110 m

(c) 200 m

(d) 220 m

159. What will be the area of a semi-circle of 14 m diameter ? (NABARD, 2002)

(a) 22 m²

(b) 77 m²

(c) 154 m²

(d) 308 m²

(e) None of these

160. A semi-circular shaped window has diameter of 63 cm. Its perimeter equals : (a) 126 cm

(b) 162 cm

(c) 198 cm

(d) 251 cm

(S.S.C. 1999)

161. What will be the area of a semi-circle whose perimeter is 36 cm ? (a) 154 cm²

(b) 168 cm²

(c) 308 cm²

(d) Data inadequate

(e) None of these

(B.S.R.B. 1998)

162. If a wire is bent into the shape of a square, then the area of the square is 81 sq. cm. When the wire is bent into a semi-circular shape, then the area of the semi-circle will be : (S.S.C. 2002)

(a) 22 cm²

(b) 44 cm²

(c) 77 cm²

(d) 154 cm²

163. The area of a sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm, is :

(a) 7.5 cm²

(b) 7.75 cm²

(c) 8.5 cm²

(d) 8.75 cm²

(S.S.C. 1999)

164. In a circle of radius 7 cm, an arc subtends an angle of 108° at the centre. The area of the sector is :

(a) 43.2 cm²

(b) 44.2 cm²

(c) 45.2 cm²

(d) 46.2 cm²

165. The area of the greatest circle which can be inscribed in a square whose perimeter is 120 cm, is :

(S.S.C. 2004)

(a) $\frac{22}{7} \times \left(\frac{7}{2}\right)^2$ cm²

(b) $\frac{22}{7} \times \left(\frac{9}{2}\right)^2$ cm²

(c) $\frac{22}{7} \times \left(\frac{15}{2}\right)^2$ cm²

(d) $\frac{22}{7} \times (15)^2$ cm²

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

(S.S.C. 2000)

(a) 49 cm²

(b) 154 cm²

(c) 378 cm²

(d) 1078 cm²

167. The area of a circle is 220 sq. cm. The area of a square inscribed in this circle will be :

(C.B.I. 1997)

(a) 49 cm²

(b) 70 cm²

(c) 140 cm²

(d) 150 cm²

168. A square is inscribed in a circle whose radius is 4 cm. The area of the portion between the circle and the square is :

(a) $(8\pi - 16)$

(b) $(8\pi - 32)$

(c) $(16\pi - 16)$

(d) $(16\pi - 32)$

169. The circumference of a circle is 100 cm. The side of a square inscribed in the circle is :

(C.B.I. 2003)

(a) $50\sqrt{2}$ cm

(b) $\frac{100}{\pi}$ cm

(c) $\frac{50\sqrt{2}}{\pi}$ cm

(d) $\frac{100\sqrt{2}}{\pi}$ cm

170. Four equal sized maximum circular plates are cut off from a square paper sheet of area 784 cm². The circumference of each plate is :

(S.S.C. 2003)

(a) 22 cm

(b) 44 cm

(c) 66 cm

(d) 88 cm

171. 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) Rs. 1560

(b) Rs. 1650

(c) Rs. 3120

(d) Rs. 3300

172. The ratio of the areas of the incircle and circumcircle of an equilateral triangle is :

(a) 1 : 2

(b) 1 : 3

(c) 1 : 4

(d) 1 : 9

173. The radius of the circumcircle of an equilateral triangle of side 12 cm is :

(a) $\frac{4\sqrt{3}}{3}$ cm

(b) $4\sqrt{3}$ cm

(c) $\frac{4\sqrt{3}}{3}$ cm

(d) $4\sqrt{3}$ cm

174. The area of the incircle of an equilateral triangle of side 42 cm is :

(S.S.C. 2004)

(a) $22\sqrt{3}$ cm²

(b) 231 cm²

(c) 462 cm²

(d) 924 cm²

175. The area of a circle inscribed in an equilateral triangle is 154 cm². Find the perimeter of the triangle.

(a) 71.5 cm

(b) 71.7 cm

(c) 72.3 cm

(d) 72.7 cm

176. The sides of a triangle are 6 cm, 11 cm and 15 cm. The radius of its incircle is :

(a) $3\sqrt{2}$ cm

(b) $\frac{4\sqrt{2}}{5}$ cm

(c) $\frac{5\sqrt{2}}{4}$ cm

(d) $6\sqrt{2}$ cm

(M.A.T. 2001)

177. The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is : (S.S.C. 2003)

(a) 70 cm²

(b) 140 cm²

(c) 210 cm²

(d) 420 cm²

178. If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is : (S.S.C. 2000) (a) 1 (b) 1.5 (c) 2 (d) 3
179. An equilateral triangle, a square and a circle have equal perimeters. If T denotes the area of the triangle, S, the area of the square and C, the area of the circle, then : (a) S < T < C (b) T < C < S (c) T < S < C (d) C < S < T (C.D.S. 2003)
180. The area of the largest triangle that can be inscribed in a semi-circle of radius r, is : (a) r² (b) 2r² (c) r³ (d) 2r³ (Section Officers', 2001)
181. ABC is a right-angled triangle with right angle at B. If the semi-circle on AB with AB as diameter encloses an area of 81 sq. cm and the semi-circle on BC with BC as diameter encloses an area of 36 sq. cm, then the area of the semi-circle on AC with AC as diameter will be : (a) 117 cm² (b) 121 cm² (c) 217 cm² (d) 221 cm²
182. If the radius of a circle is increased by 75%, then its circumference will increase by : (a) 25% (b) 50% (c) 75% (d) 100% (C.D.S. 2003)
183. 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 : (S.S.C. 2000) (a) 20 min. (b) 25 min. (c) 50 min. (d) 100 min.
184. If the radius of a circle is increased by 6%, then the area is increased by : (a) 6% (b) 12% (c) 12.36% (d) 16.64% (D.M.R.C. 2003)
185. If the radius of a circle is diminished by 10%, then its area is diminished by : (a) 10% (b) 19% (c) 20% (d) 36% (Hotel Management, 2003)
186. If the radius of a circle is doubled, its area is increased by : (C.B.I. 1998) (a) 100% (b) 200% (c) 300% (d) 400%
187. The radius of a circle is doubled, its area is increased by : (a) 100% (b) 200% (c) 300% (d) 400%
188. If the circumference of a circle increases from 4π to 8π, what change occurs in its area ? (a) It is halved. (b) It doubles. (c) It triples. (d) It quadruples. (S.S.C. 2000)
189. Three circles of radius 3.5 cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is : (S.S.C. 2003) (a) 1.967 cm² (b) 1.975 cm² (c) 19.67 cm² (d) 21.21 cm²
190. Four circular cardboard pieces, each of radius 7 cm are placed in such a way that each piece touches two other pieces. The area of the space enclosed by the four pieces is : (a) 21 cm² (b) 42 cm² (c) 84 cm² (d) 168 cm²
191. Four horses are tethered at four corners of a square plot of side 63 metres so that they just cannot reach one another. The area left ungrazed is : (a) 675.5 m² (b) 780.6 m² (c) 785.8 m² (d) 850.5 m²