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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)

In ΔOAB,

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

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

= 20

Radius (r) of circle = 20 cm

Area of quadrant OPBQ = * 3.14 * (20)^{2}

= * 3.14 * 800

= 628 cm^{2}

Area of OABC = (Side)^{2}

= (20)^{2}

= 400 cm^{2}

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

= (628 - 400)

= 228 cm^{2}

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