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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.]

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Solution

S

In ΔOAB,

\({OB} ^{2} = {OA}^{2} + {AB}^{2}

= {20}^{2} + {20}^{2} \)

OB = 202

Radius (r) of circle = OB = 202

Area of quadrant OPBQ =\90360×3.14×(202)2

14×3.14×800=628cm2

Area of OABC = Side2=202=400cm2

Area of shaded region = Area of quadrant OPBQ − Area of OABC

=(628400)cm2228cm2


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