Question

Find the area in $c{m}^2$ of the shaded region if PQ = 24cm, PR = 7cm and O is the centre of the circle. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Area of the shaded region = Area of the semi-circle with O as centre and OQ as radius - area of $\Delta PQR$

Since QR is a diameter of the circle,

$\therefore \angle RPQ={90}^{\circ }$ [Angle of semi-circle]

$\therefore {QR}^2={PR}^2+{PQ}^2=7^2+{24}^2$

$=49+576$

$=625={25}^2$

$QR=25$

$\therefore$ diameter of the circle = 25cm and radius = 12.5cm

Area of the semi-circle $=\frac{1}{2}\times \pi r^2=\frac{11\times 625}{28}$

Area of $\Delta PQR$
$=\frac{1}{2}\times PR\times PQ=84c{m}^2$

Hence area of the shaded region
$=\frac{11\times 625}{28}-84c{m}^2$

Hence area of the shaded region
$=126.64c{m}^2$