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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]
Solution
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`
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