Question

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

Answer 1

area of shaded region = area of square $-4\times$ area of sector

$=a^2-4[\pi r^2\times \frac{\theta }{360}]$

$={14}^2-4[\frac{22}{7}\times 7^2\times \frac{90}{360}]$

$=196-154=42c{m}^2$

perimeter $=4\times$ area of arc

$=4\times 2\pi r\frac{\theta }{360}$

$=4\times 2\pi \times 7\times \frac{90}{360}$

$=44c{m}^2$