# Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1 Problem 5

#### Express the area A of an equilateral triangle as a function of its side x.

SOLUTION:

From the formula of the area of a triangle, $A=\frac{1}{2}\cdot a\cdot b\cdot sin\left(\theta \right)$. Also, we know that an interior angle of an equilateral triangle is 60 degrees, and $sin\:60^{\circ} =\frac{\sqrt{3}}{2}$

$A=\frac{1}{2}\cdot x\cdot x\cdot sin\:60^{\circ}$

$A=\frac{1}{2}\cdot x^2\cdot \frac{\sqrt{3}}{2}$

$A=\frac{\sqrt{3}}{4}x^2$