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

sol: Let $\mathrm{?}ABC$ be an isosceles triangle, in which,
We have, AB = AC = 12cm ...(Given)

Now, AB + AC + BC = 30 ...(Given, perimeter = 30cm)
i.e., 12 + 12 + BC = 30
i.e., BC = 30 - 24
So, BC = 6cm
Now, we know that, $s=\frac{a+b+c}{2}$
Therefore, $s=\frac{30}{2}=15cm$

Now, Area of triangle = $\sqrt{15\left(15?12\right)\left(15?6\right)\left(15?12\right)}$ ...(Since, Heron's formula [area = $\sqrt{s\left(s?a\right)\left(s?b\right)\left(s?c\right)}$])
= $\sqrt{15×3×9×3}$
= $\sqrt{3×5×9×9}$
= $9\sqrt{15}{cm}^{2}$