An isosceles triangle has perimeter 30cm and each of the equal sides is 12cm. Find the area of the triangle.

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Solution

Let the third side of this triangle be x.
Perimeter of triangle =30 cm
12 cm +12 cm + x = 30 cm $∵$ Isosceles triangle
So, x = 6 cm

$s = \frac{P e r i m e t e r o f t r i a n g l e}{2} = \frac{30 c m}{2} = 15 c m$

By Heron’s formula,
$Area of given triangle = \sqrt{s (s - a) (s - b) (s - c)}$
$= \sqrt{15 (15 - 12) (15 - 12) (15 - 6)} c m^{2}$
$= \sqrt{15 (3) (3) (9)} c m^{2}$
$= 9 \sqrt{15} c m^{2}$

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Area of a Triangle - by Heron's Formula

Standard IX Mathematics

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