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