Question

Find the area of the shaded region in fig., if $PQ=24cm,PR=7cm$ and $O$ is the centre of the circle.

Answer 1

Area of shaded region $=$ Area of semicircle $-$ Area of $△$ $PQR$

In right-angle triangle $PQR,$ .....(Triangle in a semicircle)

By Pythagoras theorem,

$Q{P}^2+R{P}^2=R{Q}^2$

$QR=\sqrt{{24}^2+7^2}$ $=25cm$

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

Here, radius $r=\frac{25}{2}=12.5cm$

$\text{Area}=\frac{\frac{22}{7}\times 12.5\times 12.5}{2}$ $=245.54c{m}^2$
Area of $△PQR=\frac{1}{2}\times \text{Base}\times \text{Height}$ $=\frac{1}{2}\times 24\times 7$ $=84c{m}^2$
$\therefore$ Area of shaded region $=$ $245.54-84$ $=161.54c{m}^2$