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 $=36sqrt(3)" units"^2" "$ as an exact value

Area $=62.354" units"^2 " "$ 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 $" "36/3=12$

Half one side is $1/2xx12=6$

By the property of similar triangles

$12/2=h/sqrt(3)$

$h=6sqrt(3)$

Area is $1/2" base "xx"height"$

$color(blue)(=>" area "=12/2xx6sqrt(3)" "=" "36sqrt(3))$