## anonymous 5 years ago what is the area of an equilateral triangle with perimeter 12?

1. anonymous

4sqrt(3)

2. anonymous

2*

3. anonymous

^delete

4. anonymous

If the triangle is equilateral, it has three equal sides. The length of each side is then, $12/3=4$units. The area of any plane triangle is $\frac{1}{2}(base)(perpendicular.height)$(perpendicular height is perpendicular distance from base to top). You have the base. You now need the perpendicular height. If you draw an equilateral triangle and drop a line from the apex to the bottom, such that the line is perpendicular to the base, you'll have two congruent, right-angled triangles. The base of each of these triangles will be 2 and the hypotenuse, 4. You need to use Pythagoras' Theorem to solve for the height:$4^2=2^2+h^2 \rightarrow 16=4+h^2 \rightarrow h^2=12 \rightarrow$$h=\pm \sqrt{12}=\pm 2\sqrt{3}$We only take the positive solution since you're not having negative length here. So now you have everything you need: base, height, and so the area is,$A=\frac{1}{2}\times 4\times 2\sqrt{3}=4\sqrt{3}$ square units.

5. anonymous