Question

an equilateral triangle has a side length of 10 units. what is its area? type your answer in the box. square units

Explanation:

Step1: Recall the formula for the area of an equilateral triangle

The formula for the area \( A \) of an equilateral triangle with side length \( s \) is \( A=\frac{\sqrt{3}}{4}s^{2} \).

Step2: Substitute the given side length into the formula

We are given that \( s = 10 \) units. Substituting \( s = 10 \) into the formula, we get:
\( A=\frac{\sqrt{3}}{4}\times(10)^{2} \)

Step3: Simplify the expression

First, calculate \( (10)^{2}=100 \). Then, multiply by \( \frac{\sqrt{3}}{4} \):
\( A=\frac{\sqrt{3}}{4}\times100 = 25\sqrt{3}\approx25\times1.732 = 43.3 \) (if we want a decimal approximation) or we can leave it in exact form as \( 25\sqrt{3} \).

Answer:

\( 25\sqrt{3} \) (or approximately \( 43.3 \))