A child makes a poster on a chart paper drawing a square ABCD of side 14cm. 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.15.74). In the shaded region she writes a message ‘Save Energy’. Find the perimeter and area of the shaded region.
Given,
Side of square = 14cm
Radius of each circle = = 7cm
Area of square = (side)2 = 142 = 196cm2
Area of 4 quadrants of circle =
Area of shaded region = area of square – area of 4 quadrants
= 196 – 154 = 42cm2
Perimeter of shaded region = ×2πr
So, total perimeter of 4 circles = 4×11 = 44cm