Question

In the figure, a square of diagonal 8cm is inscribed in a circle. Find the area of shaded region

Answer 1

Let the side of the square $=a$

$\therefore$ Diagonal $=a\sqrt{2}$

$\Rightarrow a\sqrt{2}=8$ ........... Given

$\Rightarrow a=\frac{8}{\sqrt{2}}=4\sqrt{2}$

$\therefore$ Area of the square $={\left(4\sqrt{2}\right)}^2$

$=32c{m}^2$

Radius of the circle $=4cm$

$\therefore$ Area of circle $=\pi \times {\left(4\right)}^{2}c{m}^2$

$\therefore$ Area of shaded region $=(\pi \times {\left(4\right)}^2-32)c{m}^2$

$=(16\pi -32)c{m}^2.$

Hence, the answer is $(16\pi -32)c{m}^2.$