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Question

Four equal circles are described about four corners of a square so that each touches two of the others as shown in the fig. Find the area of the shaded portion, each side of the square measuring 28 cm.
616541_af28523e0bbc4e9e9be9f5c002edfa5e.jpg

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Solution

Let ABCD be the given square of side a.
a = 28 cm
Radius of each circle, r =282
=14cm

Area of the shaded portion = Area of a square - 4 × Area of a quadrant
=a24×14×πr2
=28×284×14×227×14×14
=784615.44

Area of the shaded portion = 168.56 cm2.

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