Find the area of the shaded region in Fig. 2, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points

Find the area of the shaded region in Fig. 2, 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 of side 12 cm. [Use π = 3.14] 

Answer

Radius of each are drawn = 6 cm 

Area of one quadrant = (3.14) x $ \frac{36}{4} $

Area of four quadrants = 3.14 x 36 = 113.04 cm²  

Area of square ABCD = 12 x 12 = 144 cm² 

Hence, Area of shaded region = 144 - 113.04

= 30.96 cm²