Question

in the adjoininh figure ABCD is a square of side 21 cm.AC andBD are two diagonals of the square.Two semicircle are drawn with AD and BC as diameters .Find the area of shaded region

Answer 1

I hope the answer is correct.

Answer 2

The area of shaded region is 576cm²

Side of square = 21cm (Given)

Let the diagonal of square = √2

Therefore, AC=BD =21 √2

AO = OC = BO = OD = 21√2/2

Area of Δ AOD = Area of ΔBOC = 1/2 × 21√2/2 × 21√2/2 = 441/4cm²

Area of semicircle = 1/2πr²

= 1/2 × 22/7 × (21/2)²

= 693/4cm²

Area of shaded region = Area of two semicircles + Area of Δ AOD + Area of ΔBOC

= 2 × 693/4 + 441/ 4 + 441/4

= 2268/4

= 576

The area of shaded region is 576cm².