Ex 12.3, 16 - Calculate the area of the designed region - Ex 12.3

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Ex 12.3, 16 Calculate the area of the designed region in figure common between the two quadrants of circles of radius 8 cm each. Area of designed region = Area of 1st quadrant + Area of 2nd quadrant – Area of square Area of 1st quadrant = 𝜃/360×𝜋𝑟2 = 90/360×22/7×82 = 1/4×22/7×8×8 = 22/7×2×8 = 352/7 cm2 For 2nd quadrant, As radius and angle are same Area of 2nd quadrant = Area of 1st quadrant = 352/7 cm2 Now , Area of square = side × side = 8 ×8 = 64 cm2 Area of designed region = Area of 1st quadrant + Area of 2nd quadrant – Area of square = (352/7+352/7−64) = ((352 +352 −64×7)/7) = ((704 −448)/7) = 256/7 cm2

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