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