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 writes a message 'Save Energy'. Find the area of the shaded region. (Use $\pi =\frac{22}{7}$)

• A. 42 $c{m}^2$
• B. 32 $c{m}^2$
• C. 12 $c{m}^2$
• D. 26 $c{m}^2$

Answer 1

The correct option is A

42 $c{m}^2$

The areas of each of the 4 sectors are equal and each sector is a quarter circle.

$\therefore$ Total area of all four sectors = area of circle.

Radius of circle = $\frac{14}{2}$ = 7 cm.

Area of circle = $\pi$ x $7^2$

​​= $\frac{22}{7}$ x $49$

= $154c{m}^2$

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

Area of the shaded portion = Area of the square ABCD – area of circle

= 196 - 154

= 42 $c{m}^2$