Question

In the given figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.         [Use  π  = 22/7] 

Answer 1

Area of each of the 4 sectors is equal to each other and is a sector of 90° in a circle of 7 cm radius.

Area of each sector =

= 1/4 x 22/7 x 7 x 7

=77/2 cm²

Area of square ABCD = (Side)² = (14)² = 196 cm²

Area of shaded portion = Area of square ABCD − 4 × Area of each sector

= 196 - 4 x 77/2 = 196 - 154

=42 cm²

Therefore, the area of shaded portion is 42 cm².