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

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Answer 1 · 2016-05-14T15:30:26

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

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

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

Tony B

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

Half one side is $\frac{1}{2} \times 12 = 6$ $1/2xx12=6$

By the property of similar triangles

$\frac{12}{2} = \frac{h}{\sqrt{3}}$ $12/2=h/sqrt(3)$

$h = 6 \sqrt{3}$ $h=6sqrt(3)$

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

$\Rightarrow area = \frac{12}{2} \times 6 \sqrt{3} = 36 \sqrt{3}$ $color(blue)(=>" area "=12/2xx6sqrt(3)" "=" "36sqrt(3))$