The sides of a triangle are 9 cm, 12 cm and 15 cm; the area of the triangle is :

1. 54 cm²

2. 96 cm²

3. 108 cm²

4. 135 cm²

Let the sides of the triangle be:

a = 9 cm, b = 12 cm and c = 15 cm.

The semi-perimeter s:

$∵ s = \dfrac{a + b + c}{2}\\[1em] = \dfrac{9 + 12 + 15}{2}\\[1em] = \dfrac{36}{2}\\[1em] = 18$

∵ Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

= $\sqrt{18(18 - 9)(18 - 12)(18 - 15)}$ cm²

= $\sqrt{18 \times 9 \times 6 \times 3}$ cm²

= $\sqrt{2,916}$ cm²

= 54 cm²

Hence, option 1 is the correct option.