Single Variable Calculus, Chapter 1, 1.1, Section 1.1, Problem 53

The problem below describes a function. Find its formula and domain.

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

An equilateral triangle is a triangle that has equal sides and internal angles, the formula of its area is...




$
\begin{equation}
\begin{aligned}

\text{Area} = \frac{1}{2}(a)(b) \sin \theta && ;\text{where } a \text{ and } b \text{ are the length of the sides and } \theta \text{ is the angle between them.}
\end{aligned}
\end{equation}
$


On the figure below shows an equilateral triangle. We can substitute its parameters to the formula of area of the triangle.









$
\begin{equation}
\begin{aligned}

\text{Area} \displaystyle = \frac{1}{2}(x)(x) \sin 60^{\circ} && (\text{Simplifying the equation})\\
\boxed{\begin{array}{llll}
\text{Area} & = & \frac{\sqrt{3}}{4} x^2\\
\text{domain:} & & x > 0
\end{array}}
\end{aligned}
\end{equation}
$