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Question
In the given figure, PQ = 24, PR = 7 cm and O is the centre of the circle. Find the area of the shaded region.
Solution
In the right ΔRPQ, we have:
`"RQ" = sqrt("RP"^2 + "PQ"^2)`
`=sqrt(7^2+24^2)`
`= sqrt(49+576)`
= 25 cm
OR = OQ = 12.5 cm
Now,
Area of the circle = πr2
= 3.14 × 12.5 × 12.5
= 490.625 sq. cm
Area of the semicircle `= 490.625/2 = 245.31 "sq.cm" `
Area of the traingle `= 1/2xx"b"xx"h" = 1/2xx7xx24=84 "sq.cm"`
Thus, we have
Area of the shaded part = Area of the semicircle - Area of the triangle]
= 245.13 - 84
= 161.31 cm2
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