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.]

Answer 1

Construction: Join OB

In right triangle AOB

OB² = OA² + AB² 

= 20² + 20²

= 400 + 400

= 800

∴ OB² = 800

Area of the shaded region = Area of quadarant OPBQ – Area of square OABC

`=1/4pi("OB")^2 - ("OA")^2`

`=1/4xx3.14xx800-400`

= 2(314) – 400

= 628 – 400

= 228 cm²

Hence, the area of the shaded region is 228 cm².