Express the area of an equilateral triangle

Express the area of an equilateral triangle as a function of the length of a side.

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,

Expanding this, we get

and solving for h, we have

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.

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