Question

In the adjoining figure, $ABCD$ is a square of side $7cm$ and two semi circles are drawn in side of it with $AB$ and $CD$ as diameter. Find the area of the shaded region in $c{m}^2$

• A. $77c{m}^2$
• B. $38.5c{m}^2$
• C. $12.25\pi c{m}^2$
• D. $49\pi c{m}^2$

Answer 1

The correct option is B $38.5c{m}^2$

Diameter of semicircle $=7cm\Rightarrow radius=\frac{7}{2}cm$

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

Area of shaded region$=2x\left(\frac{\pi r^2}{2}\right)=\pi r^2$

$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=\frac{77}{2}=38.5c{m}^2\Rightarrow \left(B\right)$