Properties of Triangles

Find the area of $\triangle ABC$ if $a = 18 \; cm$, $b = 24 \; cm$ and $c = 30 \; cm$


Area of $\triangle ABC = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$ $\;$ where $s$ is the semi-perimeter of $\triangle ABC$

$s = \dfrac{a + b + c}{2} = \dfrac{18 + 24 + 30}{2} = 36 \; cm$

$\begin{aligned} \therefore \; \text{Area of } \triangle ABC & = \sqrt{36 \left(36 - 18\right) \left(36 - 24\right) \left(36 - 30\right)} \\\\ & = \sqrt{36 \times 18 \times 12 \times 6} \\\\ & = 6 \times 3 \times 2 \times 6 \\\\ & = 216 \; cm^2 \end{aligned}$