Question

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

Answer 1

Let the third side of this triangle be x. 
Perimeter of triangle = 30 cm
\(⇒\) 30 = 12 + 12 + c
c = 30 - 24
c = 6 cm
Semi Perimeter (s) = \(\frac{P}{2}\) =\( \frac{\text{(a + b + c)}}{2}\)
s = \(\frac{30}{2}\)
s = 15 cm

Using Heron’s formula,
Area of a triangle = \(\sqrt{\text{s(s - a)(s - b)(s - c)}}\)

\(= \sqrt{\text{15(15 - 12)(15 -12)(15 - 6)}}\)

\(= \sqrt{15 × 3 × 3 × 9}\)

\(= \sqrt{1215}\)
\(= 9\sqrt{15} \) cm²

Area of the triangle \(= 9\sqrt{15} \) cm²