## Elementary Geometry for College Students (6th Edition)

$A = \frac{s^2}{4}~\sqrt{3}$
Theorem 11.4.1: The area of an acute triangle equals one-half the product of the lengths of two sides and the sine of the included angle. In an equilateral triangle, each side has the same length of $s$ and each angle has the same measure of $60^{\circ}$. We can find the area: $A = \frac{1}{2}~s \times s \times sin(\theta)$ $A = \frac{1}{2}~s^2 sin(\theta)$ $A = \frac{1}{2}~s^2 sin(60^{\circ})$ $A = \frac{1}{2}~s^2 ~(\frac{\sqrt{3}}{2})$ $A = \frac{s^2}{4}~\sqrt{3}$