Question

14. Calculate the area of the shaded portion, if P, Q, R and S are the mid-points
of the square.
​

Answer 1

Given :

Side of square = 12 cm

In figure, Four quadrants are included in the four sides of the square PAS, PBQ,RCQ, RDS.

Radius of the circle(r) = 12/2 cm = 6 cm

Area of the square ABCD = side × side = 12² = 144 cm²

Area of 1 quadrant = (π r²)/4 cm² = (3.14 × 6²/4 cm²

= 3.14 × 36 / 4 = 3.14 × 9 = 28.26cm²

Area of 4 quadrants = 4 × 28.26 cm² = 113.04 cm²

Area of the shaded region = Area of the square ABCD – Area of 4 quadrants

= 144 cm² – 113.04 cm² = 30.96 cm²

Hence, the area of the shaded region is 30.96 cm^2.