Question

In the given figure, 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 1

In ΔOAB,

OB² = OA² + AB²

= (20)² + (20)² 

OB = 20√2

Radius (r) of circle = 20√2 cm

Area of quadrant OPBQ

=  90^o/360^o x 3.14 x  (20√2)²

= 1/4 x 3.14 x 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) cm²

= 228 cm²