# Express the area of an equilateral triangle

#### Solution:

Let “x” represent the side length of the equilateral triangle. If we let “h” represent the height of the  triangle, we can use Pythagorean theorem to figure it out.

Thus,

$h^{2}+(\frac{1}{2}x)^{2}=x^{2}$

Expanding this, we get

$h^{2}=x^{2}-\frac{1}{4}x^2=\frac{3}{4}x^{2}$

and solving for h, we have

$h=\frac{\sqrt{3}}{2}x$

The area of a triangle is equal to $A=\frac{1}{2}(base)(height)$. If we write area as a function of length, then we have

$A(x)=\frac{1}{2}(x)(\frac{\sqrt{3}}{2}x)=\frac{\sqrt{3}}{4}x^{2}$ and the domain is x>0.