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 remainig circles (Fig.). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region. (Use $\pi =\frac{22}{7}$)

Answer 1

Area of each of the 4 sectors is equal to each other and is a sector of ${90}^{\circ }$ in a circle of 7 cm radius.

Area of each sector = $\frac{{90}^{\circ }}{{360}^{\circ }}$ x $\pi$ x $7^2$

​​​= $\frac{1}{4}$ x $\pi$ x $7^2$

= $\frac{77}{2}c{m}^2$

Area of square ABCD = $sid{e}^2$ = ${14}^2$= $196c{m}^2$

Area of the shaded portion = Area of the square ABCD – 4 Area of each sector

= 196 – 4 $\frac{77}{2}$

= 196 - 154

= 42 $c{m}^2$