Question

An isosceles triangle has perimeter $30$ cm and length of its congruent sides is $12$ cm. Find the area of the triangle.

Answer 1

Given the perimeter of the isosceles triangle be $30$ cm.

Also given the congruent sides are each of $12$ cm.

Then the length of the remaining side be $30-(12+12)=6$ cm.

Now the half perimeter of the triangle be $\left(s\right)=\frac{30}{2}=15$ cm.

Now using Heron's formula for a triangle, the area will be

$Area=\sqrt{15(15-12)(15-12)(15-6)}$ cm${}^2$.

$Area=9\sqrt{15}=9\sqrt{15}$ cm${}^2$.