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Ex 12.1, 4 - Find area of a triangle two sides of which are - Finding area of triangle

  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise
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Ex 12.1, 4 Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm. Area of triangle = √(s(s−a)(s−b)(s −c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Given a = 18 cm, b = 10 cm and Perimeter = 42 cm Semi-Perimeter = s =Perimeter/2 s = 42/2 s = 21 cm We need to find c Now, Perimeter = 42cm a + b + c = 42 cm 18 cm + 10 cm + c = 42 cm 28 cm + c = 42 cm c = 42 – 28 cm c = 14 cm Area of triangle = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) Putting a = 18 cm, b =10 cm, c = 14 cm & s = 21 cm Area of triangle =√(21(21 −18)(21 −10)(21 −14)) = √(21(3)(11)(7)) = √(21 (7 ×3)(11)) = √(21 (21)(11)) = √("21 × 21" ) × √11 = √("21" 2) × √11 = (21) ×√11 = 21 √11 Thus , Area = 21 √11 cm2

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