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.
Perimeter of triangle =30 cm
12 cm +12 cm + x = 30 cm $\because$ Isosceles triangle
So, x = 6 cm

$s=\frac{Perimeteroftriangle}{2}=\frac{30cm}{2}=15cm$

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