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Question

A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles (in the following figure). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region.
(Use π = 22/7)

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Solution

Perimeter of the shaded portion = 4 ⨯ Length of the arc having central angle 90
=4×90°360°×2×227×142=4×14×2×227×7=44 cm
Area of shaded portion = Area of square ABCD − 4 ⨯ Area of the arc having central angle 90
=142-4×90°360°×227×1422=196-4×14×227×72=196-154=42 cm2

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