Question

Find the area of the shaded region in figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD (Use π = 3.14).

Answer 1

Given, side of a square BC = 12 cm

Since, Q is a mid-point of BC.

∴ Radius = BQ = `12/2` = 6 cm

Now, area of quadrant BPQ

= `(pi"r"^2)/4`

= `(3.14 xx (6)^2)/4`

= `113.04/4 "cm"^2` 

Area of four quadrants

= `(4 xx 113.04)/4`

= 113.04 cm²

Now, area of square ABCD

= (12)²

= 144 cm²

∴ Area of the shaded region

= Area of square – Area of four quadrants

= 144 – 113.04

= 30.96 cm²