Sum

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

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#### Solution

Radius = 5 cm

AB = BC = CD = AD = 10 cm

All sides are equal, so it is a square.

Area of a square = Side^{2}

Area of the square = 10^{2 }= 100 cm^{2}

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

`= 1/4xx22/7xx5xx5`

= 19.64 cm^{2 }

Area of the quadrants of four circles = 19.64 × 4 = 78.57 cm^{2}

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

= 100 - 78.57 cm^{2}

= 21.43 cm^{2}

Concept: Area of Circle

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