Question

In the given figure, $RSTV$ is a square inscribed in a circle with centre $O$ and radius $r$. The total area of the shaded region is _______.

• A. $r^2(\pi -2)$
• B. $2r^2(2-\pi )$
• C. $\pi (r^2-2)$
• D. $8r^2-8r$

Answer 1

The correct option is A $r^2(\pi -2)$

Area of shaded region is Area of circle $-$ Area of square.

Area of circle $=\pi r^2$

Area of square $=\frac{1}{2}{d}^2$ where $d$ is diameter

$=\frac{1}{2}(2r{)}^2$

$=2r^2$

$\therefore$ Area of shaded region $=\pi r^2-2r^2$=r^2(\pi -2)$