Question

Four equal circles, each of radius 5 cm, touch each other, as shown in the figure. Find the area included between them.

Answer 1

Radius = 5 cm

AB = BC = CD = AD = 10 cm

All sides are equal, so it is a square.

Area of a square = Side²

Area of the square = 10²  = 100 cm²

Area of the quadrant of one circle `= 1/4 pi"r"^2` 

`= 1/4xx22/7xx5xx5`

= 19.64 cm² 

Area of the quadrants of four circles = 19.64 × 4 = 78.57 cm²

Area of the shaded portion = Area of the square - Area of the quadrants of four circles

= 100 - 78.57 cm²

= 21.43 cm²