Question

In given figure, ABCD is a rectangle, having $AB=20$ cm and $BC=14$ cm. Two sectors of ${180}^{\circ }$ have been cut-off. Calculate the area of the shaded region.

Answer 1

Given $AB=20$ cm and $BC=14$ cm

$\Rightarrow$ Area of rectangle $ABCD=AB\times BC=20\times 14$

$\therefore$ Area of rectangle $ABCD=280c{m}^2$

$\Rightarrow$ Here, two semicircle present in rectangle with diameter $14cm$.

$\Rightarrow$ Radius of semicircle $\left(r\right)=\frac{14}{2}=7cm$

$\Rightarrow$ Area of $2$ semicircle $=2\times \frac{\pi r^2}{2}$

$\Rightarrow$ Area of $2$ semicircle $=2\times \frac{22\times (7{)}^2}{2\times 7}$

$\therefore$ Area of $2$ semicircle $=154c{m}^2$

$\Rightarrow$ Area of shaded region = Area of rectangle $ABCD$ - Area $2$ semicircle

$\Rightarrow$ Area of shaded region $=280-154=126c{m}^2$