Question

Find the area of the shaded region in the given figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle. [Use Π = 22/7]

Answer 1

It can be observed that RQ is the diameter of the circle. Therefore, ∠RPQ will be 90º.

By applying Pythagoras theorem in ΔPQR,

RP² + PQ² = RQ²

(7)² + (24)² = RQ²

`RQ = sqrt625 = 25`

Radius of circle, OR = RQ/2 = 25/2

Since RQ is the diameter of the circle, it divides the circle in two equal parts.

Area of semi circle RPQOR = `1/2 pir^2`

`= 1/2pi(25/2)^2`

`=1/2xx22/7xx625/4`

`=6875/28 cm^2`

Area of ΔPQR = `1/2 xx PQ xxPR`

`= 1/2 xx 24 xx 7`

= 84 cm²

Area of shaded region = Area of semi-circle RPQOR − Area of ΔPQR

= 6875/28 - 84

`= (6875 - 2352)/28`

`= 4523/28 cm^2`