Answer :

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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