How do you work out the area of an equilateral triangle with sides of length 6cm? How do you work out the area of an equilateral triangle with sides of length 6cm?

1 Answer
mason m
Dec 1, 2015

#9sqrt3" cm"^2#

Explanation:

jwilson.coe.uga.edu

We can see that if we split an equilateral triangle in half, we are left with two congruent equilateral triangles. Thus, one of the legs of the triangle is #1/2s#, and the hypotenuse is #s#. We can use the Pythagorean Theorem or the properties of #30˚-60˚-90˚# triangles to determine that the height of the triangle is #sqrt3/2s#.

If we want to determine the area of the entire triangle, we know that #A=1/2bh#. We also know that the base is #s# and the height is #sqrt3/2s#, so we can plug those in to the area equation to see the following for an equilateral triangle:

#A=1/2bh=>1/2(s)(sqrt3/2s)=(s^2sqrt3)/4#

Thus, since #s=6" cm"#, the area is #(6^2sqrt3)/4" cm"^2# or #9sqrt3" cm"^2#.

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