Question

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. [CBSE 2011]

Answer 1

Permieter of shaded region = Length of the arc APB + Length of the arc CPD + Length of AD + Length of BC
$$\begin{gathered} =\frac{1}{2}\times 2\mathrm{\pi }r+\frac{1}{2}\times 2\mathrm{\pi }r+14+14 \\ =2\mathrm{\pi }r+28 \\ =2\times \frac{22}{7}\times \frac{14}{2}+28 \\ =72\mathrm{cm} \end{gathered}$$

Hence, the perimeter of the shaded region is 72 cm.