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Example 1 - Find area of triangle, two sides are 8 cm - Examples

  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise
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Example 1 Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 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 = 8 cm, b = 11 cm and Perimeter = 32 cm Semi-Perimeter = s =Perimeter/2 s = 32/2 s = 16 cm We need to find c Now, Perimeter = 32 cm a + b + c = 32 cm 8 + 11 + c = 32 19 + c = 32 c = 32 – 19 c = 13 cm Area of the triangle = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) Putting a = 8 cm , b = 11cm , c = 13 cm & s = 16 cm Area of given triangle = √(16×(16−8)×(16−11)×(16−13)) = √(16×8×5×3) cm2 = √((8×2)×8×5×3) = √((8×8)×2×5×3) = √(8×8)×√( 2×5×3) = √82×√30 = (8) ×√30 = 8 √30 Thus, Area = 8 √30 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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