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Ex 12.3, 3 - If ABCD is a square of side 14 cm and APD - Area of combination of figures : circle based

  1. Chapter 12 Class 10 Areas related to Circles
  2. Serial order wise
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Transcript

Ex 12.3, 3 Find the area of the shaded region in figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles. Area of shaded region = Area of square ABCD – Area of semicircle APD – Area of semicircle BPC Area of square ABCD Side of square = 14 cm Area of square = Side × Side = 14 × 14 = 196 cm2 Area of semi circle APD Diameter = AD = 14 cm So, radius = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 14/2 = 7 cm Area of semi circle APD = 1/2 πr2 = 1/2×22/7×7^2 = 1/2×22/7×7×7 = 77 cm2 Similarly, For semicircle BPC Diameter = BC = 14 cm Since diameter is same Area of semi circle BPC = Area of semi circle APD = 77 cm2 Now, Area of shaded region = Area of square – Area of semi circle APB – Area of semi circle BPC = 196 – 77 – 77 = 196 – (77 + 77) = 196 – (154) = 42 cm2 Hence, area of shaded region = 42 cm2

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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