Question

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

Answer 1

Given, PQ = 24 cm, PR = 7 cm

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

Here, ∠RPQ = 90°

In ΔRPQ,

RQ² = PR² + PQ²   ...(By Pythagoras theorem)

⇒ RQ² = (7)² + (24)²

= 49 + 576

= 625

∴ RQ = 25 cm

∴ Area of ΔRPQ

= `1/2 xx RP xx PQ`

= `1/2 xx 7 xx 24`

= 84 cm²

And area of semi-circle = `1/2 xx πr^2`

= `1/2 xx 22/7 xx (25/2)^2`

= `(11 xx 625)/(7 xx 4)`

= `6875/28` cm

Now, area of shaded region = Area of sem-circle – Area of ΔRPQ

= `6875/28 - 84`

= `(6875 - 2352)/28`

= `4523/28`

= 161.54 cm²