Question

A square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.

Answer 1

Given,

Side of the square = 21 cm = OA

Area of the square = OA² = 21² = 441 cm²

Diagonal of the square OB = √2 OA = 21√2 cm

And, from the fig. its seen that

The diagonal of the square is equal to the radius of the circle, r = 21√2 cm

So, the area of the quadrant = 1/4 πr² = 1/4 (22/7)(21√2)² = 693 cm²

Thus,

The area of the shaded region = Area of the quadrant – Area of the square

= 693 – 441

= 252 cm²