Q. 134.4( 217 Votes )

In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)


Answer :

In ΔOAB,

OB2 = OA2 + AB2


= (20)2 + (20)2


= 20


Radius (r) of circle = 20 cm


Area of quadrant OPBQ = × 3.14 × (20)2


= × 3.14 × 800


= 628 cm2


Area of OABC = (Side)2


= (20)2


= 400 cm2


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


= (628 - 400)


= 228 cm2

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