Question

Three equal circles, each of radius 6 cm, touch one another as shown in the figure. Find the area of enclosed between them.

Answer 1

Join ABC. All sides are equal, so it is an equilateral triangle.
Now,
Area of the equilateral triangle `=sqrt(3)/4xx"Side"^2`

`= 1.73/4xx12xx12`

= 62.28 cm² 

Area of the arc of the circle`=60/360pi"r"^2`

`= 1/6pi"r"^2`

`=1/6xx22/7xx6xx6`

= 18.86 cm²

Area of the three sectors = 3 × 18.86 = 56.57 cm² 

Area of the shaded portion = Area of the triangle -- Area of the three quadrants

= 62.28 - 56.57

= 5.71 cm²