Question

Calculate the area other than the area common between two quadrants of circles of radius 16 cm each, which is shown as the shaded region in the given figure.

Answer 1

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{shaded}\mathrm{region}=\mathrm{Ar}\left(\mathrm{square}\mathrm{ABCD}\right)-\mathrm{Ar}\left(\mathrm{quadrant}\mathrm{ABED}\right)+\mathrm{Ar}\left(\mathrm{square}\mathrm{ABCD}\right)-\mathrm{Ar}\left(\mathrm{quadrant}\mathrm{CDFB}\right) \\ ={16}^2-\frac{1}{4}{\mathrm{\pi r}}^2+{16}^2-\frac{1}{4}{\mathrm{\pi r}}^2 \\ =512-\frac{1}{2}\mathrm{\pi }\times 16\times 16 \\ =512-402.3 \\ =109.7{\mathrm{cm}}^2 \end{gathered}$$