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Ex 12.3, 7 - ABCD is a square of side 14 cm. With centres - Ex 12.3

  1. Chapter 12 Class 10 Areas related to Circles
  2. Serial order wise
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Ex 12.3, 7 In figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. Since square has all angles 90° Area of shaded region = Area of square ABCD – Area of 4 quadrants of circles Area of square ABCD Given side of square = 14 cm Area of the square = (Side)2 = (14)2 = (14 × 14) = 196 cm2 Area of 4 quadrants of circles In the question, diagram shows symmetry ∴ radius of the circle would be equal. In every single diagrams radius = (𝑆𝑖𝑑𝑒 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒)/2 = 14/2 = 7 So, radius = r = 7 cm Now , Area of one quadrant = 1/4 × Area of circle = 1/4 𝜋𝑟2 = 1/4×22/7×(72) = 1/4×22× (7 ×7) = 1/4×22× 49 = 154/4 cm2 Area of 4 quadrants = 4 × area of quadrant = 4 ×154/4 = 154 cm2 Area of shaded region = Area of square - Area of 4 quadrant = 196 – 154 = 42 cm2 Hence, area of shaded region = 42 cm2

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