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ABCD is a square with a 14-cm side in the illustration. Four circles are drawn with centres A, B, C, and D, so that each circle touches two of the remaining three circles on the outside. Find the shaded region's area.

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40 c m 2

42 c m 2

44 c m 2

46 c m 2

answer is A.

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Detailed Solution

Given that ABCD is a square with sides 14cm.
Question Image

Four circles are drawn with A, B, C and D as centre respectively.
Radius of circle = 7 cm.
Find the area of square
Area of square

= (s i d e) 2

⇒ A r e a = 142 ⇒ A r e a = 196 c m 2

Area of quadrant

= 14 π r 2

Area of 4 quadrants of circles

⇒ A r e a = 4 × 14 × π r 2 ⇒ A r e a = 227 × 72 ⇒ A r e a = 22 × 7 ⇒ A r e a = 154 c m 2

Area of shaded region = Area of square – Area of 4 quadrants of circles

⇒ A r e a = 196 − 154 ⇒ A r e a = 42 c m 2

Area of shaded region

= 42 c m 2

.
Therefore the answer is option (2).

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