What is the area of an equilateral triangle with side length 14?

##49sqrt3##

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 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=14##, the area of the triangle is ##(14^2sqrt3)/4=(196sqrt3)/4=49sqrt3##.