Question

In the Figure 6, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Answer 1

Solution

Area of the shaded region = Area of Square ABCD − (Area of semicircle APD + Area of semicircle BPC)
=(14)2−[12π(142)2+12π(142)2]=(14)2−227(7)2=42 cm2
$$\begin{gathered} ={\left(14\right)}^2-\left[\frac{1}{2}\mathrm{\pi }{\left(\frac{14}{2}\right)}^2+\frac{1}{2}\mathrm{\pi }{\left(\frac{14}{2}\right)}^2\right] \\ =196-154 \\ =42{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area of the shaded region is 42 cm².