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

Answer 1

Nathan Axel

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:

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))#

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Answer 2

Ethan Adkins

[ \text{{Area of equilateral triangle}} = \frac{{\sqrt{3}}}{4} \times \left(\frac{{\text{{Perimeter}}}}{3}\right)^2 ]

Substitute the given perimeter value: [ \text{{Area}} = \frac{{\sqrt{3}}}{4} \times \left(\frac{{36}}{3}\right)^2 ]

Calculate the result.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.