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