Q41 of 45 Page 12

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.

(CBSE 2015)

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

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