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Ex 12.3, 11 - On a square handkerchief, nine circular designs - Area of combination of figures : circle based

  1. Chapter 12 Class 10 Areas related to Circles
  2. Serial order wise
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Ex 12.3, 11 On a square handkerchief, nine circular designs each of radius 7 cm are made (see figure). Find the area of the remaining portion of the handkerchief. Area of remaining portion = Area of square – Area of 9 circles Here, handkerchief is made up of contributing 9 circles. So, Side of square = 3 × Diameter of circle Here, Radius of circle = 7 cm Diameter of circle = 7 × 2 = 14 cm So, Side of square = 3 × 14 = 42 cm Area of square = (side)2 = (42)2 = 42 × 42 = 1764 cm2 Area of one circle = 𝜋𝑟2 = 𝜋(7)^2 = 22/7×7×7 = 22×7 = 154 cm2 Area of 9 circles = 9 × Area of one circle = 9 × 154 = 1386 cm2 Area of remaining portion = Area of square – Area of 9 circles = 1764 – 1386 = 378 cm2 Hence, Area of remaining portion = 378 cm2

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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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