# How do you find the area of an equilateral triangle if the perimeter is 36ft?

May 14, 2016

Area $= 36 \sqrt{3} \text{ units"^2" }$ as an exact value

Area $= 62.354 \text{ units"^2 " }$ to 3 decimal places

#### Explanation:

Being able to visualise a problem quite often helps so it is good practice to do a quick sketch:

The perimeter is 36. There are three equal length sides so one side is $\text{ } \frac{36}{3} = 12$

Half one side is $\frac{1}{2} \times 12 = 6$

By the property of similar triangles

$\frac{12}{2} = \frac{h}{\sqrt{3}}$

$h = 6 \sqrt{3}$

Area is $\frac{1}{2} \text{ base "xx"height}$

$\textcolor{b l u e}{\implies \text{ area "=12/2xx6sqrt(3)" "=" } 36 \sqrt{3}}$