Examples

Chapter 10 Class 9 Herons Formula
Serial order wise

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### Transcript

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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.