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 away that each circle touches externally two of the three remaining circles (Fig.,). In the shaded region she writes a message ‘Save Energy’. Find the perimeter and area of the shaded region

(use π = \(\frac{22}7\))

Answer 1

Given, 

Side of square = 14 cm 

Radius of each circle = \(\frac{14}2\) = 7cm 

Area of square = (side)² = 14² = 196 cm² 

Area of 4 quadrants of circle = \(\frac{90}{360}\times\frac{22}7\times7\times7\)

= \(4\times\frac{1}{4}\times154\) =154 cm²

Area of shaded region = area of square – area of 4 quadrants 

= 196 – 154 = 42 cm²  

Perimeter of shaded region = \(\frac{90}{360}\) × 2πr 

= \(\frac{1}4\times2\times\frac{22}7\times7\) = 11 cm

So, 

total perimeter of 4 circles = 4 × 11 = 44 cm