Question

find the area of the shaded region if PQ= 24 cm PR =7 cm and O is the centre of the circle given.
please help me​

Answer 1

It is clear from the figure that PQ is the diameter of the circle O.

Angle subtended by diameter is a right angle.

So ∠PRQ is 90°

So ΔPRQ is right angled triangle.

PQ² = PR² + QR²

24² = 7² + QR²

QR² = 527

$QR = \sqrt{527}$

Area of ΔPRQ = $\frac{1}{2}PR*QR$

$= \frac{7\sqrt{527} }{2}$

Area of semicircle PQR = $\frac{\pi r^2 }{2}$ = $72\pi$ cm²

So the area of the shaded region = $(72\pi- \frac{7\sqrt{527} }{2} ) cm^2$