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Ex 12.1, 6 - An isosceles triangle has perimeter 30 cm - Finding area of triangle


  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise
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Ex 12.1, 6 An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle. 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 triangle is isosceles In isosceles triangle, two sides are equal So, a = b = 12 cm and Perimeter = 30 cm Semi-Perimeter = s =Perimeter/2 s = 30/2 s = 15 cm We need to find c Perimeter = 30cm a + b + c = 30 cm 12 cm+ 12 cm + c = 30 cm 24 + c = 30 c = 30 – 24 c = 6 cm Area of triangle = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) Putting a = 12 cm, b =12 cm, c = 6 cm & s = 15 cm = √(15(15−12)(15−12)(15−6)) = √(15(3)(3)(9)) = √(15 (9)(9)) = √("9" ×9) ×√15 = √("92" ) ×√15 = (9) ×√15 = 9 √15 Thus, Area = 9 √15 cm2

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