1. One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field. (120m

^{2})2. A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The area of the lawn is (1/6) hectares. Find the length and breadth of the lawn. (33 1/3 and 50)

3. Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs. 12.40 per square metre. (1934.4)

4. If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle. (120)

5. The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.(20)

6. In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements. (0.8)

7. A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre.(680)

8. The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. (24)

9. A room 5m 55cm long and 3m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.(176)

10. Find the area of a square, one of whose diagonals is 3.8 m long. (7.22)

11. The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.(4:25)

12. If each side of a square is increased by 25%, find the percentage change in its area.(56.25)

13. 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. Find the perimeter of the original rectangle. (50)

14. A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.(6)

15. Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm.(84)

16. Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.(30)

17. The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.(300)

18. The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triangle. (60)

19. Find the length of the altitude of an equilateral triangle of side 3√3 cm. (4.5)

20. In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases. (16:9)

21. The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height. (6)

22. Find the area of a rhombus one side of which measures 20 cm and 01 diagonal 24 cm.(384)

23. The difference between two parallel sides of a trapezium is 4 cm. perpendicular distance between them is 19 cm. If the area of the trapezium is 475 find the lengths of the parallel sides.(27 and 23)

24. Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq. metres. (56)

25. The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre. (5808)

26. The diameter of the driving wheel of a bus is 140 em. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph?(250)

27. A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel. (14)

28. The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle. (84)

29. Two concentric circles form a ring. The inner and outer circumferences of ring are 50 2/7m and 75 3/7m respectively. Find the width of the ring. (4)

30. A sector of 120′, cut out from a circle, has an area of 9 3/7sq. cm. Find the radius of the circle. (3)

31. Find the ratio of the areas of the in circle and circumcircle of a square.(1:2)

32. If the radius of a circle is decreased by 50%, find the percentage decrease in its area.(75)

EXERCISE

1. 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?(56)

2. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:(2520)

3. 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. (16,500)

4. 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? (126)

5. 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? (7.2)

6. 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(2560)

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?

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?(37500)

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?(2:1)

10. 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:(30)

11. 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 :(153600)

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?

13. 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: (87.5)

14. 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? (40)

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: (20X5)

16. 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? (315)

17. 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? (18)

18. A rectangular plot is half as long again as it is broad and its area is 23 hectares. Then, its length is: (100)

19. The diagonal of the floor of a rectangular closet is 7 ½ feet. The shorter side of the closet is 4 ½ feet. What is the area of the closet in square feet? (27)

20. The length of a rectangle is three times of its width. If the length of the diagonal 8√10 cm is then the perimeter of the rectangle is : (64)

21. 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: (7.5)

22. 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? (140)

23. 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: (20000)

24. A rectangular carpet has an area of 120 sq. metres and a perimeter of 46 metres. The length of its diagonal is: (17)

25. 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: (60)

26. The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be: (18)

27. The diagonal of a rectangle is thrice its smaller side. The ratio of the length to the breadth of the rectangle is: (2√2 : 1)

28. 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: (12)

29. 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? (40)

30. 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: (40)

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

32. 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: (28, 20)

33. 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’? (88)

34. 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?

35. 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: (28)

36. 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. (20)

37. 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?

38. The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area? (50% increase)

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? (37 ½ )

40. 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 (64)

41. A room is 15 feet long and 12 feet broad. A mat has to be placed on the floor of this room leaving 1 ½ feet space from the walls. What will be the cost of the mat at the rate of Rs. 3.50 per square feet? (378)

42. 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? (2)

43. 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. (data inadequate)

44. 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 travelling the roads at 75 paise per sq. metre is: (258)

45. 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? (3440)

46. 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? (3)

47. A housing society has been allotted a square piece of land measuring 2550.25 sq. m. What is the side of the plot? (50.5)

48. 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(124)

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: (900)

50. 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: (120)

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: (225)

52. 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? (16)

53. What is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad? (814)

54. 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?

55. The perimeter of a square is 48 cm. The area of a rectangle is 4 cm 2 less than the, area of the square. If the length of the rectangle is 14 cm, then its perimeter is: (48)

56. The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is 3/2 times that of the side of the square, then the side of the square is : (20)

57. 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: (30, 10)

58. 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? (73,800)

59. A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road?(600)

60. A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? (30)

61. Man walking at the speed of 4 kmph crosses a square field diagonally in 3 minutes. The area of the field is: (20000)

62. If the length of the diagonal of a square is 20 cm, then its perimeter must be : (40√2)

63. The area of a square field is 69696 cm2. Its diagonal will be, equal to: (373.296)

64. 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? (60)

65. 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? (6:5)

66. A square and a rectangle have equal areas. If their perimeters are p1 and p2 respectively, then: (p1 < p2)

67. 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 > B)

68. The diagonal of a square is 4√2cm. The diagonal of another square whose area is double that of the first square, is: (8)

69. The ratio of the area of a square to that of the square drawn on its diagonal, is: (1:2)

70. The ratio of the areas of two squares, one having its diagonal double than the other, is:(4:1)

71. If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is: (15:16)

72. 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: (9:4)

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: (201)

74. What happens to the area of a square when its side is halved? Its area will: (1/4)

75. 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: (4.04)

76. If the area of a square increases by 69%, then the side of the square increases by : (30)

77. If the diagonal of a square is made 1.5 times, then the ratio of the areas of two squares is(4:9)

78. 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: (82)

79. 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? (100)

80. The difference of the areas of two squared 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. (9)

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: (14)

82. 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. (34)

83. 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: (558)

84. 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: (474)

85. 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: (1900)

86. 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: (4)

87. The base of a triangle is 15 cm and height is 12 cm. The hieight of another triangle of double the area having the base 20 cm is: (18)

88. The area of a right-angled triangle is 4Q times its base. What is its height? (80)

89. If the area of a triangle is 1176 cm2 and base : corresponding altitude is 3 : 4, then the altitude of the triangle is (56)

90. The area of a triangle is 216 cm2 and its sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is: (72)

91. 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: (3/2)

92. One side of a right angled triangle is twice the other, and the hypotenuse is 10 cm. The area of the triangle is: (20)

93. The perimeter of a right-angled triangle is 60 cm. Its hypotenuse is 26 cm. The area of the triangle is: (120)

94. 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? (5)

95. If the perimeter of an isosceles right triangle is (6 + 32√2) m, then the area of the triangle is(4.5)

96. If the area of an equilateral triangle is 24√3 sq. cm, then its perimeter is : (12√6)

97. The three sides of a triangle are 5 cm, 12 cm and 13 cm respectively. Then, its area is (3/2)