Q3 of 27 Page 228

Find the area of the shaded region in each of the following figures.


[Hint: d + +=42]


d = 21


∴ side of the square 21 cm

The shaded region is formed of four semicircles and as the base of these semicircles lie on the side of a square, therefore the diameter of the semicircle is equal to the side of the square.

⇒ diameter of semicircle = side of square = d



It is shown that, r + d + r = 42



⇒ d = 21 cm



⇒ Radius, r = 10.5 cm




⇒ A = 173.25 sq.cm


Area of shaded region = 4 × (Area of semicircle)


⇒ 4 × A


⇒ 4 × 173.25


⇒ 693 sq.cm


∴ Area of the shaded region is 693 sq.cm


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 3

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 4

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