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 = `90^@/360^@ xx pi(7)^2`

`=1/4xx22/7xx7xx7`

`= 77/2 cm^2`

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 xx 77/2 = 196 - 154`

`= 42 cm^2`

Therefore, the area of shaded portion is 42 cm².