In fig., ABCD is a square of side 14 cm. With centers A, B, C, and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.

The square ABCD touches 4 circles and forms 4 quadrants which can be seen in the figure. Since, AE=ED=AF=FB=BG=GC=CH=HD=1/2 × Side of Square = Common radius ∴ Radius = 7cm Since, Area of Square ABCD = 14 × 14 = 196 cm2 And, area of Quadrants (Sectors) = θ/360 × π × r2 = 4 × 90/360 × π × 7 × 7 = 154 cm2 ∴ Area of Shaded region = Area of ABCD - Area of 4 Quadrants = 196 - 154 = 42 cm2