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Answer :

Let \(\triangle{ABC}\) be an isosceles triangle, in which,

We have,

AB = AC = 12cm ...(Given)

Now, AB + AC + BC = 30

(Given, perimeter = 30cm)

\(\Rightarrow \)
12 + 12 + BC = 30

\(\Rightarrow \) BC = 30 - 24

\(\Rightarrow \) 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 = \(\sqrt{s(s - a)(s - b)(s - c)}\)])

= \(\sqrt{15 × 3 × 9 × 3}\)

= \(\sqrt{3 × 5 × 9 × 9}\)

= \(9\sqrt{15} {cm}^2\)

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