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

Example 1 - Chapter 12 Class 9 Herons Formula - Part 2
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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.