Question

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

Answer 1

Let the third side of this triangle be $x.$
$a=12cm,$ b $=12cm,$ c $=xcm$

Perimeter of triangle $=30cm$

$\Rightarrow$ $12cm$ + $12cm$ + $x=30cm$

$\Rightarrow x=30-24$

$\therefore x=6cm$

Semi-perimeter, $s=\frac{\text{Perimeter of triangle}}{2}=\frac{30}{2}=15cm$

By Heron’s formula,

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{15(15-12)(15-12)(15-6)}$

$=\sqrt{15\left(3\right)\left(3\right)\left(9\right)}$

$=9\sqrt{15}c{m}^2$
Hence, the area of the isosceles triangle is $9\sqrt{15}c{m}^2$.