Question

If the side of an equilateral triangle is $8\text{cm}$, then find its area.

Answer 1

• The area $A$ of an equilateral triangle with side $s$ is given by $A=\frac{\sqrt{3}}{4}{s}^2$.

Step 1: Substitute $s=8$ into the formula $A=\frac{\sqrt{3}}{4}{s}^2$ and find the area of triangle.

$\begin{array}{rcl}A& =& \frac{\sqrt{3}}{4}{\left(8\right)}^2\\ & =& \frac{\sqrt{3}}{4}\times 8\times 8\\ & =& \sqrt{3}\times 2\times 8\\ & =& 16\sqrt{3}{\text{cm}}^2\end{array}$

Hence, the area of an equilateral triangle is $\begin{array}{rcl}& & 16\sqrt{3}{\text{cm}}^2\end{array}$.