Find the perimeter of shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.

Given:

Side of square = 14 cm

Diameter of semi circle = 14 cm

⇒ Radius of semi circle = = 7 cm

∵ There are 2 semi circles of same radius.

∴ We consider it as one circle with radius 7 cm.

So,

Perimeter of 2 semicircles = Perimeter of circle = 2πr

= 2 × × 7

= 2 × 22 = 44 cm

Perimeter of shaded region = Perimeter of 2 semicircles + 2 × Side of Square = 44 + 2 × 14 = 44 + 28 = 72 cm

__Hence, the area of the shaded region is 72 cm.__

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