Question

If the sides of ∆ABC are 18 cm, 15 cm and 15 cm long, find its area.

Answer 1

Length of the sides of the triangle are 18 cm, 15 cm and 15 cm.
Semi-perimeter of a triangle$=s=\frac{a+b+c}{2}$
Semi-perimeter$=\frac{18+15+15}{2}=24\mathrm{cm}$
Area of a triangle$=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$
$$\begin{gathered} =\sqrt{24\left(24-18\right)\left(24-15\right)\left(24-15\right)} \\ =\sqrt{24\left(6\right)\left(9\right)\left(9\right)} \\ =\sqrt{11664} \\ =108{\mathrm{cm}}^2 \end{gathered}$$

∴ Area of the triangle is 108 cm²