Question

an equilateral triangle has side lengths of 6 units. what is the triangles area?

a) 18 square units

b) 36 square units

c) $9\sqrt{3}$ square units

d) $18\sqrt{2}$ square units

Explanation:

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

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

Step2: Substitute the given side length into the formula

We are given that the side length \( s = 6 \) units. Substituting \( s = 6 \) into the formula, we get:
\( A=\frac{\sqrt{3}}{4}\times(6)^{2} \)

Step3: Simplify the expression

First, calculate \( (6)^{2}=36 \). Then,
\( A=\frac{\sqrt{3}}{4}\times36 \)
Simplify \( \frac{36}{4}=9 \), so \( A = 9\sqrt{3} \) square units.

Answer:

c) \( 9\sqrt{3} \) square units