In Fig. 2, 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)

Construction: Join OB.

Let us consider ΔAOB,

By Pythagoras Theorem,

OB² = OA² + AB²

Given, side of square OA = 20 cm.

∴ OB² = 20² + 20²

OB² = 800

OB = 20√2 cm

Thus, radius of circle, r = 20√2 cm

We know that area of quadrant = (θπr²)/360°

So, area of quadrant OQBP = (90° × π × (20√2)²)/360°

= 200 × 3.14

= 628 cm²

We know that area of square = (side)²

So, area of square OABC = (20)²

= 400 cm²

Thus, area of Shaded region = Area of Quadrant OQBP – Area of square OABC

= (628 – 400) cm²

= 228 cm²

Ans. The area of shaded region is 228 cm².