Question

In adjoining fig two semicircles are drawn on sides $AD$ and $BC$ of a square $ABCD$. If $AB=10cm,(\pi =3.14)$, then the area of shaded portion is :

• A. $21.5c{m}^2$
• B. $22c{m}^2$
• C. $22.5c{m}^2$
• D. $24.25c{m}^2$

Answer 1

The correct option is A $21.5c{m}^2$

Radius of the two semicircle $=$ $\frac{10}{2}$ $=$ $5cm$
Therefore, area of the two semicircle $=$ $\pi (5{)}^2$
$=$ $3.14\times 25$
$=$ $78.50$ sq.cm
Side of square $AB=10cm$
Area of square $=$ $($side${)}^2$
$=$ $(10{)}^2$
$=$ $100$ sq.cm
Therefore, area of shaded region $=$ Area of square $-$ Area of semi circles
$=$ $(100-78.50)$ sq.cm
$=$ $21.5$ sq.cm