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25/06/2021 1:39 pm
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Find the area of the shaded region in Figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
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25/06/2021 1:41 pm
Here, P is in the semi-circle and P = 90°
So, it can be concluded that QR is hypotenuse of the circle and is equal to the diameter of the circle.
∴ QR = D
Using Pythagorean theorem,
QR2 = PR2 + PQ2
QR2 = 72 + 242
QR= 25 cm = Diameter
Hence, the radius of the circle = 25/2 cm
Now, the area of the semicircle = (πR2)/2
= (22/7) × (25/2) × (25/2)/2 cm2
= 13750/56 cm2 = 245.54 cm2
Also, area of the ΔPQR = 1/2 × PR × PQ
=(1/2) × 7 × 24 cm2
= 84 cm2
Hence, the area of the shaded region = 245.54 cm2 - 84 cm2
= 161.54 cm2