Q15 of 35 Page 311

Nitu has drawn a square ABCD of which length of each side as 12 cm. My sister has drawn four circular arcs with length of radius 6 cm. centering A, B, C, D like picture besides and she has designed some portion. Let us write by calculating the area of shaded region.

Given, each side of square = 12cm


⇒ Area of Square ABCD = side2


⇒ (12)2


⇒ 144cm2


Let Radius of each quadrant be r


⇒ r = 6 cm (given)


Now, the sum of the area of the four quadrants at the four corners of the square


⇒ 4 × area of each quadrant ( area of circle = πr2where r is the radius)


⇒ area of quadrant =


⇒


⇒


⇒ 113.14cm2


Now, area of shaded portion


= Area of square, ABCD - sum of the areas of four quadrants at the four corners of the square


⇒ 144 – 113 .14 cm2


= 30 .86 cm2


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