# 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,

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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