# What is the area of an equilateral triangle whose perimeter is 48 inches?

Aug 5, 2018

Answer: $64 \sqrt{3}$ ${\text{in}}^{2}$

#### Explanation:

Consider the formula for the area of an equilateral triangle:
$\frac{{s}^{2} \sqrt{3}}{4}$, where $s$ is the side length (this can be easily proved by considering the 30-60-90 triangles within an equilateral triangle; this proof will be left as an exercise for the reader)

Since we are given that the perimeter of the equilateral trangle is $48$ inches, we know that the side length is $\frac{48}{3} = 16$ inches.

Now, we can simply plug this value into the formula:
$\frac{{s}^{2} \sqrt{3}}{4} = \frac{{\left(16\right)}^{2} \sqrt{3}}{4}$

Canceling, a $4$ from the numerator and the denominator, we have:
$= \left(16 \cdot 4\right) \sqrt{3}$
$= 64 \sqrt{3}$ ${\text{in}}^{2}$, which is our final answer.