Question

What is the area of an equilateral triangle with side lengths of `8sqrt2` cm?

Answer 1

`32sqrt3` `cm^2`

Explanation:

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`

Since, in your case, `s=8sqrt2`, the area of your triangle is:

`((8sqrt2)^2sqrt3)/4=(64*2*sqrt3)/4=32sqrt3cm^2`