Question

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

Answer 1

As angle in a semi-circle is ${90}^{\circ }\Rightarrow \angle RPQ={90}^{\circ }$

Area of shaded region = Area of semicircle - ar(QRP)

$=\frac{1}{2}\pi r^2-\frac{1}{2}\left(RP\right)\left(QP\right)$

In $△RQP,R{Q}^2=P{R}^2+P{Q}^2=576+49$

$\Rightarrow R{Q}^2=625\Rightarrow RQ=25cm\Rightarrow 2r=25cm$

$\Rightarrow$ Area of shaded region = $\frac{1}{2}(\frac{\pi \times 625}{4}-7\times 24)$

$=\frac{1}{2}(490.6-168)$

$=161.3c{m}^2$