Question

The height of an equilateral triangle measures $9$ cm. Find its area, correct to $2$ places of decimal. Take $3=1.732$.

Answer 1

Given height of the equilateral triangle $=9$ cm
Thus, we have:
Height is $=\frac{\sqrt{3}}{2}\times$Side
$\Rightarrow 9=\frac{\sqrt{3}}{2}\times$ Side
$\Rightarrow \text{Side}=\frac{3\times 3\times 2}{\sqrt{3}}$
$\Rightarrow \text{Side}=\frac{\sqrt{3}\times \sqrt{3}\times 6}{\sqrt{3}}$
$\therefore \text{Side}=6\sqrt{3}$ cm
Also,
Area of equilateral triangle $=\frac{\sqrt{3}}{4}\times (\text{Side}{)}^2$
$=\frac{\sqrt{3}}{4}\times (6\sqrt{3}{)}^2$
$=\frac{\sqrt{3}}{4}\times 108$
$=27\times \sqrt{3}$
$=46.76c{m}^2$
Hence, the area of given triangle is $=46.76c{m}^2$