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

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Solution

Given:

Side of a square(AB=BC=AD=CD) = 14 cm

Diameter of circle= side of square= 14 cm

Radius of circle= = 7cm

Perimeter of the shaded region = side of AD + side of BC+ length of Semicircle APB + length of Semicircle CPD

Perimeter of the shaded region = 14+14+ +πr+πr

=28+ 2πr

= 28 + 2()× 7

= 28 + 44

= 72 cm

Hence, the Perimeter of the shaded region = 72 cm.

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