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

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

= \(\sqrt{15 × 3 × 9 × 3}\)
= \(\sqrt{3 × 5 × 9 × 9}\)
= \(9\sqrt{15} {cm}^2\)