Problems on Area

1. Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has larger area and by how much?

(a) Square 33 cm²

(b) Circle 33 cm²

(c) both have equal area

(d) Square

Answer: (b)

Explanation:

Perimeter of square = 44 cm

∴ side of square = 11 cm

Area of square =121 cm²

Circumference of circle = 44 cm

Area of circle =

Hence circle has larger area by 154 – 121 =33 cm².

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2. The area (in sq cm) of the largest circle that can be drawn inside a square of side 28 cm is

(a) 17248

(b) 784

(c) 8624

(d) 616

Answer: (d)

Explanation:

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3. A wire is in the form of a circle of radius 42 cm. if it is bent into a square, then the side of the square will be:

(a) 60 cm

(b) 62 cm

(c) 64 cm

(d) 66 cm

Answer: (d)

Explanation:

Perimeter of square = circumference of circle

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4. Three circles of radius 3.5 cm each are placed in such a way that each touches the other two. The area of the portion enclosed by the circles is:

(a)

(b) 

(c)

(d) 

Answer: (b)

Explanation:

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5. ABCD is the square of sides 12 cm. At the four corners, four circles were drawn with the diameter of 2 cm each. A circle with 6 cm radius was drawn in the center of the square. What is the area of the shaded portion?

(a) 27.714 cm²

(b) 33.765cm²

(c) 53.763 cm²

(d) 80.432 cm²

Answer: (a) 

Explanation:

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6. The quadrants shown in figure are each of diameter 12 cm. what is the area of the shaded portion?

(a) 

(b)

(c)  

(d) 

Answer: (d)

Explanation:

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7. The boundary of the shaded region in the given diagram consists of three semi circular areas, the small ones being equal. The diameter of the larger circle is 12 cm. Find the area of the shaded region.

(a) 34.98cm²

(b) 56.57 cm²

(c) 65.67cm²

(d) 71.25 cm²

Answer: (b)

Explanation:

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8. 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.

(a)

(b) 

(c)  

(d) 

Answer: (c)

Explanation:        

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9. A right- angled triangle, having an area of, is inscribed in a circle of radius 6.5 cm. the ratio of longest side to the shortest side is:

(a) 2.4

(b) 2.5

(c) 2.6

(d) 2.8

Answer: (c) 

Explanation:

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

(a) 

(b)

(c)

(d) 

Answer: (a)

Explanation: