Answer :

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 = $\sqrt{15(15?12)(15?6)(15?12)}$ ...(Since, Heron's formula [area = $\sqrt{s(s?a)(s?b)(s?c)}$])
= $\sqrt{15\times 3\times 9\times 3}$
= $\sqrt{3\times 5\times 9\times 9}$
= $9\sqrt{15}{cm}^2$