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Question
In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14.]
Solution
Construction: Join OB
In right triangle AOB
OB2 = OA2 + AB2
= 202 + 202
= 400 + 400
= 800
∴OB2 = 800
Area of the shaded region = Area of quadarant OPBQ - Area of square OABC
`=1/4pi("OB")^2 - ("OA")^2`
`=1/4xx3.14xx800-400`
= 628 - 400
= 228 cm2
Hence, the area of the shaded region is 228 cm2.
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