Question

In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are
semicircles. [CBSE 2012]

Answer 1

Area of the shaded region = Area of Square ABCD − (Area of semicircle APD + Area of semicircle BPC)
$$\begin{gathered} ={\left(14\right)}^2-\left[\frac{1}{2}\mathrm{\pi }{\left(\frac{14}{2}\right)}^2+\frac{1}{2}\mathrm{\pi }{\left(\frac{14}{2}\right)}^2\right] \\ ={\left(14\right)}^2-\frac{22}{7}{\left(7\right)}^2 \\ =42{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area of the shaded region is 42 cm².