Area



AREA
AREA OF PLANE FIGURES – I
General Information
Area:
The area of any figure is the amount of surface enclosed within its bounding lines.

Perimeter:
            The perimeter of a geometrical figure is the total length of the sides enclosing the figure

TYPE 1: SQUARE
          Two dimensional form of Cube is called as square

Area=   (or)       
Area=
Diagonal=
Perimeter=4a

 

 

TYPE 2: TRIANGLE

 

Area of the triangle= 
Area of the triangle,
∆= 
where s=
Perimeter of the triangle
Radius of in circle of a triangle=

 

(a) Right angled triangle:
Area=                                            

 

 

Hypotenuse, d=     (Pythagoras theorem)
Perimeter=

 

(b) Isosceles Right-angled triangle
 

Area=
Hypotenuse, d=
Perimeter=

 

 (c) Equilateral Triangle
 

 

AD = h =
Area =
Perimeter=
Radius of in circle of an equilateral triangle of side a= 
Radius of circumcircle of an equilateral triangle of side a=

 

TYPE 3: RECTANGLE
Two dimensional form of Cuboid is called as Rectangle.            
 

Area=
Diagonal=                                 
Perimeter=
Area of 4 walls=

 

TYPE 4: CIRCLE
Two dimensional form of Sphere is called as Circle.        
 

R = Radius
D = Diameter=
Area=
Circumference=

 

TYPE 5: RHOMBUS
All sides are equal and opposite angles are equal.
 Diagonals bisect each other at right angles.

 

Area=
Side= 
Perimeter =

 

TYPE 6: PARALLELOGRAM
          Opposite sides are parallel and equal and opposite angles are equal.

 

b

  


Area = Base × Height = b × h
Perimeter = 2(a+b)

 

TYPE 7: TRAPEZIUM
            Any of the two set of opposite sides is parallel.
         

 

Area =  

 

SOLVED EXAMPLES:
1. The ratio of the areas of two squares, one having its diagonal double than the other is:                                                                                                                         [Asst. Grade 1997]
(a) 2: 3         (b) 2:1          (c) 3: 1         (d) 4: 1        
Ans: (d) 4: 1
Explanation:
Let us take diagonal of square 2 is equal to twice of diagonal of square 1.

The ratio of their area is,


 

2. If three sides of a triangle are 6 cm, 8 cm, and 10 cm, then the altitude of the triangle using the largest side as base will be:                                                                                    [CDS 2000]
(a) 8 cm        (b) 6 cm        (c) 4.8 cm     (d) 4.4 cm
Ans: (c) 4.8 cm
Explanation:

Area of ∆ABC     


24

BP = 4.8 cm

 

3. If length of the rectangle is increased by 50% and breadth is decreased by 20%. Then what is the percentage change in the area?                                                                         [Bank 2000]
(a) 20% decrease     (b) 20% increase      (c) 80% increase      (d) 30% decrease
Ans: (b) 20% increase
Explanation:
% change in area =
Here x is change in length (50%) and y is change in breadth (-20%)
=

Hence result is +ve, so, area is 20% increased.

 

4. The area of a circle is 38.5 sq m. Its circumference (in cm) is:                   [SSC Grad. 1999]
(a) 22   (b) 24     (c) 26      (d) 32
Ans: (a) 22
Explanation:
Area =


Circumference=  

 

5. If the diagonal of rhombus is 12 and 18 cm. Find the perimeter?                          [CDS 2001]
(a)                  (b)            (c)              (d)
Ans: (c)
Explanation:
D22 = 4 
182 = 4
182 = 4
P2 =
P = 12 cm

 

6. Find the area of parallelogram whose two adjacent sides are 13, 14 and length of diagonal is 15?
[SSC Grad. 2001]
(a) 42 m2      (b) 168 m2     (c) 8 m2    (d) 324 m2
Ans: (b) 168 m2
Explanation:         
S =  =  = 21
Area = 2
= 2
= 8 = 168 m2

 

7. The cross- section of a canal is in the shape of a trapezium. The canal is 15 m wide at the top and 9 m a wide at the bottom. If the area of the cross-section is 720, then the depth of the canal is:
 [CDS 2001] 
(a) 58.4m      (b) 58.6 m     (c) 58.5 m     (d) 60 m                
Ans: (d) 60m
Explanation:
 

Area of cross - section of canal


 

AREA OF PLANE FIGURES – II
General Information
This chapter contains problems involved two or more shapes in it.

 

 

SOLVED EXAMPLES:
1. Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has larger area and by how much?                                                                                      [Bank 2008]
(a) Square,    (b)    (c) both have equal area  (d) Square,
Ans: (b) Circle,
Explanation:
Perimeter of square = 44 cm
∴ side of square = 11 cm
Area of square =
Circumference of circle = 44 cm

Area of circle =
Hence circle has larger area by 154 – 121 =

 

2. Four equal-sized maximum circular plates are cut off from a square paper sheet of area 784 sq cm. the circumference of each plate is:                                                                          [SSC Grad. 2003]
(a) 22 cm      (b) 44 cm      (c) 66 cm      (d) 88 cm
Ans: (b) 44 cm
Explanation:
 

Side of square =
Radius of each circle =
∴ Circumference of each circle =  

 

3. A rectangle of certain dimensions is chopped off from one corner of a larger rectangle as shown. AB= 8 cm and BC=4cm; the perimeter of the figure ABCPQRA (in cm) is:             [Asst. Grade 1998]

(a) 36           (b) 24           (c) 48           (d) can’t be determined
Ans: (b) 24
Explanation:
Clearly, in rectangle PQRS, PS= QR = x and SR = PQ = y
 

∴ perimeter of the figure = AB +BC + (CP +x) + (y +AR)
= AB+ BC + CS + SA
= 2(l + b) = 2 (8 + 4) = 24 cm

 

4. The quadrants shown in figure are each of diameter 12 cm. what is the area of the shaded portion?                                                                                                                   [CDS 2006]  

(a)        (b)    (c)          (d)        
Ans: (d)
Explanation:

Area of the shaded figure =

 

5. ABCD is a square of side 1 unit and B, D are center of two circles of radius 1 unit. The area of shaded portion in the given diagram is.                                                                                            [CDS 2001]

 

(a)        (b)       (c)      (d)
Ans: (c)
Explanation:
Area of shaded portion = area of the two sectors – area of shaded square
=

 

 

EXERCISE:
1. Area of a regular hexagon of unit length
Ans:  sq. units

 

2. If D, E and F are respectively the middle points of the sides BC, CA and AB of a triangle ABC and the area of the triangle ABC is 24 sq.cm, then the area of the triangle DEF (in sq. cm) is
Ans: 6

 

3. If the circumference of a circle is 352m, then its area in m2 is
Ans: 9856

 

4. If the diagonal of rectangle is 17 cm long and the perimeter of the rectangle is 46 cm, then the area of the rectangle is
Ans: 120 sq. cm

 

5. The three sides of a triangle are 3 cm, 4 cm and 5 cm respectively. Then is area (in sq. cm)
Ans: 6

 

6. The perimeter of an isosceles triangle is 14 cm and the lateral side is to the base in the ratio 5:4. The area of the triangle (in sq. cm) is to
Ans:

 

7. If the area of an equilateral triangle is  sq. cm, then its perimeter is
Ans:

 

8. The ratio between the area of a square of side α and an equilateral triangle of side α is
Ans:

 

9. If x is the length of a median of an equatorial triangle, then its area is
Ans:

 

10. The altitude of an equatorial triangle of side  is
Ans: 4.5 cm

 

11. A triangle of area (a × y) cm2 has been drawn such that its area is equal to the area of an equilateral triangle of side 6 cm. Then, the value of y is
Ans:

 

12. If the area of a triangle with base α is equal to the area of a square with side α, then the altitude of the triangle is
Ans: 2

 

13. The area of a right angled triangle is 30 sq. cm and the length of its hypotenuse is 13 cm. The length of the shorter side is
Ans: 5 cm

 

14. In ∆ABC, we have BC= 5 cm, AC= 12 cm and AB= 13 cm. The length of the altitude drawn from B on AC is
Ans: 5 cm

 

15. The area of the square field is 1568m2. Find the length of its diagonal
Ans: 56 m

 

16. The areas of a rectangle and a square are in the ratio 3:4. The length of the rectangle is 8 cm more than that of the square. The breadth of the rectangle is 8 cm less than that of square. Find the perimeter of the square
Ans: 64 cm

 

17. The floor of the room is 25 cm long 16 cm wide. The cost of one hundred bricks 20 cm by 10 cm is Rs. 31. Find the total cost of furnishing the floor of the room by bricks
Ans: Rs. 6200

 

18. The perimeter of two squares are 40cm and 32 cm. Find the perimeter of a third square whose area is equal to different of the area of two squares
Ans: 24cm

 

19. The perimeter of a rhombus is 146 cm and one of its diagonal is 55 cm. Find the area of the rhombus
Ans: 1320cm2

 

20. The perimeter of a rectangle and a square are 160 m each. The area of the rectangle is less than that of the square by 100 sq.m. The length of the rectangle
Ans: 50 m

 

21. If the areas of a circle and a square are equal, then the ratio of their perimeters is
Ans:

 

22. The diagonal of a square is  cm. The diagonal of another square, whose area is double that of the first square, is?
Ans: 8 cm

 

23. A square and an equilateral triangle are drawn on the same base. The ratio of their areas is
Ans:

 

24. 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 circle? (Take )
Ans: 616 sq.cm

 

25. By melting a solid lead sphere of diameter 12 cm, three small spheres are made whose diameters are in the ratio 3:4:5. The radius (in cm) of the smallest sphere is
Ans: 3

 

26. The area of circle whose radius is 6 cm is trisected by two concentric circles. The radius of the smallest circle is
Ans:

 

27. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 80%, the volume of the cone
Ans: Decreases by 25%

 

28. If the difference between the circumference and diameter of a circle is 30 cm, then the radius of the circle must be
Ans: 7 cm

 

29. In an isosceles triangle, the measure of each of equal sides is 10 cm and the angle between them is 45°. The area of the triangle is
Ans:

 

30. A circular wire of diameter 42 cm is bent in the form of a rectangle whose sides are in the ratio 6:5. The area of the rectangle is
Ans: 1080 cm2

 

31. If the radius of a right circular cyclinder is decreased by 50% and its height is increased by 60%, its volume will be decreased by
Ans: 60%

 

32. If the sides of an equilateral triangle are increased by 20%, 30% and 50% respectively to form a new triangle, the increase in the perimeter of the equilateral triangle is
Ans:

 

33. If each side of a rectangle is increased by 50%, its area will be increased by
Ans: 125%

 

34. The floor of a corridor is 100 m long and 3 m wide. Cost of covering the floor with carpet 50 cm wide at the rate of Rs. 15 per m is
Ans: Rs. 9000

 

35. The area of a triangular field, the lengths of whose sides are 50 m, 78 m and 112 m, is
Ans: 1680 m2

 

36. The sides of a triangle are in the ratio 3:4:6. The triangle is?
Ans: obtuse-angled

 

37. The measure of each of two opposite angles of a rhombus is 60° and the measure of one of its sides is 10 cm. The length of its sides is 10 cm. The length of its smaller diagonal is
Ans: 10 cm

 

38. In a triangular field having sides 30 cm, 72 m and 78 m, the length of the altitude to the side measuring 72 m is?
Ans: 30 m

 

39. If the perimeter of a right-angled isosceles triangle is cm, the length of the hypotenuse is
Ans: 4 cm

 

40. The areas of two equilateral triangles are in the ratio 25:36. Their altitudes will be in the ratio
Ans: 5:6

 

41. If the difference between areas of the circumcircle and the incircle of an equilateral triangle is 44 cm2, then the area of the triangle is (Take
Ans:

 

42. A wire, when bent is the form of a square, encloses a region having area 121 cm2. If the same wire is bent into the form of a circle, then the area of the circle is (Take )
Ans: 154 cm2

 

43. If the area of a circle inscribed in a square is 9π cm2, then the area of the square is
Ans: 36 cm2

 

44. ABC is an equilateral triangle of a side 2 cm. With A, B, C as centres and radius 1 cm three arcs are drawn. The area of the region within the triangle bounded by the three arcs is
Ans:

 

45. If S denotes the area of the curved surface of a right circular cone of height hand semi vertical angle α then S equals
Ans: πh2sec α tan α

 

46. Each side of rectangular field is diminished by 40%. By how much percent is the area of the field diminished?
Ans: 64

 

47. The height of an equilateral triangle is  cm. The ratio of the area of its circum circle to that of its in-circle is
Ans: 4:1

 

48. A wire when bent in the form of an equilateral triangle encloses a region having area of  cm2. If the same wire is rebent into the form of a circle, its radius will be (Take )
Ans: 10.5 cm

 

49. If the perimeter of a semicircular field is 144 m, then the diameter of the field is (Take )
Ans: 56 m

 

50. The sides of a triangle are 6 cm, 8 cm and 10 cm. The area of the greatest square that can be inscribed in it, is
Ans:  cm2

 

51. The perimeter (in meters) of a semicircle is numerically equal to its area (in square metres). The length of its diameter (Take
Ans:  metres

 

52. If S1 and S2, be the surface are of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal to
Ans:  S2

 

53. The base of a conical tent is 19.2 metres in diameter and its height is 2.8 metres. The area (in square metres) of the canvas required to put up such a text is nearly (Take )
Ans: 301.71

 

54. The height and the radius of the base of a right circular cone are 12 cm and 6 cm respectively. The radius of the circular cross-section of the cone cut by a plane parallel to its base at a distance of 3 cm from the base is
Ans: 4.5 cm 

 

55. If the circumference and area of a circle are numerically equal, then the diameter is equal to
Ans: 4

 

56. The diameter of a toy wheel is 14 cm. What is the distance travelled by it in 15 revolutions?
Ans: 660 cm

 

57. The area of the ring between two concentric circles, whose circumferences are 88 cm and 132 cm, is
Ans: 770 cm2

 

58. The perimeters of a square and a circular field are the same. If the area of the circular field is 3,850 sq meters, what is the area (in m2) of the square?
Ans: 3,025

 

59. If the length of a rectangle is increased by 25 per cent and the width is decreased by 20 per cent, then the area of the rectangle
Ans: remains unchanged

 

60. The length of a rectangular garden is 12 metres and its breadth is 5 meters. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden
Ans:

 

61. 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
Ans: 18 cm

 

62. A hemisphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surfaces will be
Ans:

 

63. Three solid metallic spheres of diameters 6 cm, 8 cm and 10 cm are melted and recast into a new solid sphere. The diameter of the new sphere is
Ans: 12 cm

 

64. The sum of length, breadth and depth of a cuboid is 19 cm and its diagonal is  cm. Its surface area would be
Ans: 236 cm2

 

65. The area of a right-angled triangle is two-third of the area of a rectangle. The base of the triangle is 80 per cent of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm, what is the height of the triangle?
Ans: Data inadequate

 

66. If the length of the diagonal of a square and that of the side of another square are both 10 cm, the ratio of the area of the first square to that of the second is
Ans: 1:2

 

67. The perimeter of a rectangular field is 480 metres and the ratio between the length and breadth is 5:3, the area is
Ans: 13500 sq. m

 

68. The sides of a triangle are in the ratio  If the perimeter of the triangle is 52 cm, the length of the smallest side is
Ans: 12 cm

 

69. If the area of a triangle is 1,176 cm2 and base: corresponding altitude is 3:4, then the altitude of the triangles is 52 cm, the length of the smallest side is
Ans: 9 cm

 

70. The floor of a rectangular room is 15 m long and 12 m wide. The room is surrounded by a verandah of width 2m on all the sides. The area of the verandah is
Ans: 124 m2

 

71. What chance in per cent is made in the area of a rectangle by decreasing its length and increasing its breadth by 5%?
Ans: Decrease 0.25%

 

72. A wire bent in the form of a circle of radius 42 cm is cut and again bent in the form of a square. The ratio of the regions enclosed by the circle and the square in the two cases is given by
Ans: 14:11

 

73. The radius of a circle is 20 cm. Three more concentric circles are drawn inside it, in such a manner that it is divided into four parts of equal area. The radius of cone of the three concentric circles is
Ans:

 

74. The ratio between the length and the perimeter of a rectangular plot is 1:3 and the ratio between the breadth and perimeter of that plot is 1:6. What is the ratio between the length and area of that plot?
Ans: Data inadequate

 

75. The ratio of the area of two squares, one having its diagonal double than the other, is
Ans: 4:1

 

76. 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
Ans: 7,000

 

77. The diagonals of a rhombus are 24 cm and 10 cm. The perimeter of the rhombus (in cm) is
Ans: 52

 

78. The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. The area of the triangle is
Ans: 48 cm2

 

79. A sector of 120° cut out from a circle, has an area of  sq. cm. The radius of the circle is
Ans: 3.0

 

80. 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? (Take
Ans: 616 sq. cm

 

81. The sides of a triangle measure 4 cm, 3.4 cm, 2.2 cm. Three circles are drawn with centres at A, B and C in such a way that each circle touches the other two. Then the diameters of these circles would means (in cm)
Ans: 1.6, 2.8, 5.

 

82. The diagonals of a rhombus are 32 cm and 24 cm respectively. The perimeters of the rhombus is
Ans: 80 cm

 

83. The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2 Taking
, the height of the mountain is
Ans: 2.4 km

 

84. In the given figure, ABCD is a rectangle and area of the ∆ABE is 33 sq cm. What is the area of both the shaded portions together?

Ans: data inadequate

 

 

85. A rectangular field has dimensions 25 m by 15 m. Two mutually perpendicular passage, 2 m width have been left in its central part and grass has been grown in rest of the field. The areas (in sq meters) under the grass is
Ans: 299

 

86. The sides of a triangle are in the ratio  and its perimeter is 104 cm. The length of the longest side (in cm) is
Ans: 48

 

87. Square ABCD is inscribed in a circle with centre at O. OP ⊥ CD OP =1. Area of the shaded portion is
 

Ans: 2π-4

 

88. The length and breadth of a rectangular ball are 40 m and 30 m respectively. What is the distance between two opposite corners of the half?
Ans: 50 m

 

89. The area of the larger square is a2 and that of smaller square is b2, then the ratio of area of the shaded portion to the larger square

Ans:

 

90. The inner and outer radii of a circular track are respectively 21 m and 28 m. The cost of leveling the track at Rs. 5 per sq m is (in rupees)
Ans: 5390

 

91. The area (in sq cm) of the regular hexagon whose perimeter is 12 cm, is
Ans:

 

92. In the adjoining figure, the ratio of the areas of the parallelogram ABCD and that of triangle ABN is
 

Ans: 8:1

 

93. A shed has a side wall of the dimensions as shown below. Calculated the area of the wall in square feet

Ans: 30

 

94. What is the area of the region enclosed by the area below?

Ans: 176

 

95. If the ratio of the circumference of two circles is 2:3, then the ratio of their areas is
Ans: 4:9

 

96. An isosceles triangle of area 12 sq cm has one of its equal sides as 5 cm. The length of the base of the triangle (in cm) is
Ans: 6

 

97. PQRS is a trapezium (not drawn to scale) PQ is parallel to SR. This trapezium circumscribes a circle as shown. If another circle circumscribes the trapezium PQRS, determine the length of SR. Given that PQ=16 and QR=20
 

Ans: 24

 

98. The figure below represents a parking lot that is 30 m by 40 m and an attached driveway that has an outer radius of 20 m and an inner radius of 10 m. If the shaded region is not included, what is the area, in square metres of the lot and driveway?

Ans: 1200+150 π

 

99. A parallelogram has two sides 50 cm and 78 cm and a diagonal 112 cm long. Find the area of the parallelogram
Ans: 3360 cm2

 

100. Find the area of the unshaded portion of the figure which consists of three semi-circular regions. Given that the bigger semi-circle has a radius of 10 cm and that R bisects PQ

 

101. Find the area of a parallelogram whose base is 36 m and the corresponding altitude is 6 m
Ans: 216 m2

 

102. The length of a rope by which a buffalo must be tethered so that she may be able to graze a grassy area of 2464 sq m is
 

Ans: 28 m

 

103. The radius of the wheel of a vehicle is 35 cm. The wheel makes 20 revolutions in 10 s. The speed of the vehicle is
Ans: 15.84 km/h

 

104. The radius of a wheel is 14 dm. How many times does it revolve during a journey of 0.88 km?
Ans: 1000

 

105. A wheel makes 2000 revolutions in covering a distance of 44 km. The diameter of the wheel is
Ans: 28 m

 

106. A circular garden has a circumference of 352 m. There is a 7 m wide border inside the garden along its periphery. The area of the border is
Ans: 2310 m3

 

107. If the radius of a circle is increased by 10%, then its area is increased by
Ans: 21%

 

108. The perimeter of a rhombus is 40 cm and the length of its smaller diagonal is 12 cm. The length of the longer diagonal is
Ans: 16 cm

 

109. The area of a rhombus is 81 cm2 and one of the diagonal is double the other, the lengths of its diagonals are
Ans: 9 cm, 18 cm

 

110. The diagonals of a rhombus are 40 cm and 32 cm. Its area is
Ans: 640 cm2

 

111. The area of the largest triangle that can be inscribed in a circle of radius 8 cm is
Ans:

 

112. The sides of a triangle are in the ratio  If the perimeter is 171 cm, then the length of the longest side is
Ans: 81 cm

 

113. A circle and a rectangle have the same perimeter. The sides of the rectangle are 24 cm and 20 cm. What is the radius of the circle?
Ans: 14 cm

 

114. The area of the largest circle that can be drawn inside a square of side 28 cm is
Ans: 616 cm2

 

115. The area of four walls of a room is 66 m2. The breadth and height of the room are 4 m and 3 m respectively. The length of the room is
Ans: 6 m

 

116. The cost of cultivating a square field at the rate of Rs. 250 per hectare is Rs. 1000. The cost of putting a fence around it at Rs. 12 per m is
Ans: 9600

 

117. If each side of square is increased by 3 m, then its area is increased by 81 cm2. The side of the square is
Ans: 12 cm

 

118. The largest size of bamboo that can be placed in a square of area 324 sq m is
Ans:

 

119. The total cost of flooring a room at Rs. 12.50 per sq m is 400. If the length of the room is 8 m, its breadth is
Ans: 4 m

 

120. Four horses are tethered at four corners of a square plot of 42 m so that they just cannot reach one another. The area left ungrazed is
Ans: 378 m2

 

121. In the following figure, the area in (cm2) is
Ans: 115.5

 

122. The area of a circular field is 124.74 hectares. The cost of fencing it at the rate of 80 paise per m is
Ans: Rs. 3168

 

123. If the circumference of a circle is increased by 20%, then its area will be increased by
Ans: 44%

 

124. The sum of the radius and the circumference of a circle is 51 cm. The area of the circle is
Ans: 154 cm

 

125. The inner circumference of a circular path around a circular lawn is 440 m. What is the radius of the outer circumference of the path, if the path is 14 m wide?
Ans: 84 m

 

126. If the circumference of a circle is 704 cm, then its area is
Ans: 39424 m2

 

127. Area of a rhombus is 256 cm2. One of the diagonal is half of the other diagonal. The sum of the diagonal is
Ans: 48 cm

 

128. If the perimeter of a rhombus is 4 p and lengths of its diagonals are a and b, then its area is
Ans:

 

129. The distance of a 24 cm long side of a parallelogram from the opposite side is 22 cm. The area of the parallelogram is
Ans: 528 cm2

 

130.  A parallelogram has sides 30 cm and 20 cm and one of its diagonal is 40 cm long. Then, its area is
Ans:

 

131. The adjacent sides of a parallelogram are 6 cm and 8 cm and the angle between them is 30°. What is the area of the parallelogram?
Ans: 24 cm2

 

132. If every sides of triangle is doubled, then increase in area of the triangle is
Ans: 300%

 

133. A ladder is resting with one end in contact with the top of a wall of height 60 m and the other end on the ground is at a distance of 11 m from the wall. The length of the ladder is
Ans: 61 m

 

134. The integral base of an isosceles triangle can be whose area is 60 cm2 and the length of the one of the equal sides is 13 cm
Ans: 10 cm

 

135. The sides of a triangle are 25 m, 39 m and 56 m respectively. Find the perpendicular distance from the vertex opposite to the side 56 m
Ans: 15 m

 

136. What is the area of the triangle whose sides are 84 m, 80 m and 52 m?
Ans: 2016 sq m

 

137. The length and breadth of a square are increased by 60% and 40% respectively. The area of the resulting rectangle exceeds the area of the square by
Ans: 124%

 

138. The ratio of the area of a square to that of the square drawn on its diagonal is
Ans: 1:2

 

139. If the side of square is increased by 20%, then how much per cent does its area get increased
Ans: 44%

 

140. The length of a rectangle is 2 cm more than its breadth. The perimeter is 48 cm. The area of the rectangle (in cm) is
Ans: 143

 

141. If 90 g paint is require for painting a door 12 cm × 9 cm, how much paint is required for painting a similar door 4 cm × 3 cm?
Ans: 10

 

142. How many tiles 20 cm by 40 cm will be required to pave the floor of a prayer hall of a room 16 m long and 9 m wide
Ans: 1800

 

143. If a roll of paper 1 km long has area 1/25 hectare, how wide is the paper?
Ans: 0.4 m

 

144. A square field of 2 sq km is to be divided into two equal parts by a wall which coincides with a diagonal. Find the length of the wall
Ans: 2 km

 

145. If the length of a rectangular field is doubled and its breadth is halved (ie, reduced by 50%). What is the percentage change in its area?
Ans: 0%

 

146. If the number of square inches in the area of a square is equal to the number of inches of its circumference, then diagonal of the square will be
Ans: 4

 

147. If 85 concrete blocks each of length 25 cm, breadth 15 cm, height 10 cm are laid touching the length sides, in single layer, on the floor, how much total area of the floor in sq metres would it occupy?
Ans: 3.1875

 

148. The area of the circle centred at (1.2) and passing through (4.6) is
Ans: 25 π

 

149. Find the area of a square ABCD in square units whose three veriticies A, B and C are points (3,2), (9,2) and (9,8) respectively
Ans: 36 sq unit

 

150. The parallel sides of a trapezoid are 8 m and 6 m and its altitude is 3 cm. Find the area of trapezoid
Ans: 21 m2

 

151. The radius of a circular wheel is  m. How many revolutions will it make in travelling 11 km?
Ans: 1000

 

152. Find the area and perimeter of a triangle whose sides are 17 cm, 8 cm and 15 cm long
Ans: 60 cm2, 40 cm

 

153. Find the area of equilateral triangle whose side is
Ans:

 

154. The base of a right angled triangle is 8 cm and hypotenuse is 17 cm. Find the area?
Ans: 60 cm2

 

154. A rectangular grassy lawn is 18 m × 12 m. It has a gravel path 1.5 m wide all around it on the outside. What is the area of the path?
Ans: 99 m2

 

155. The length of a rectangle is 1 cm more than its breadth. The diagonal is 29 cm. Find the area of the rectangle
Ans:  420 cm2




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