Question

Find the area of the shaded region in figure, if $PQ=24cm,PR=7cm$ and $O$ is the centre of the circle.
(use $\pi =\frac{22}{7}$)

Answer 1

Since, QR is diameter

It forms a semi-circle

We know that angle in a semicircle is a right angle.

Hence, $\angle RPQ={90}^o$

Now,

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

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

$QR=\sqrt{625}$

$QR=25cm$

Diameter $=QR=25cm$

Radius $r=\frac{25}{2}cm$

Area of semicircle $=\frac{1}{2}\times \pi r^2$

$=\frac{1}{2}\times \frac{22}{7}\times \frac{25}{2}\times \frac{25}{2}$

$=\frac{6875}{28}c{m}^2$

Area of $△PQR=\frac{1}{2}\times PQ\times PR$

$=\frac{1}{2}\times 24\times 7$

$=84c{m}^2$

Area of shaded region $=\frac{6875}{28}-84$

$=\frac{6875-2352}{28}$

$=\frac{4523}{28}c{m}^2$