Identify given parameters

The height of the equilateral triangle is given as $h = 6$ cm.

$h = 6$

Apply Area formula

The area of an equilateral triangle in terms of its height $h$ is given by the formula $\text{Area} = \frac{h^2}{\sqrt{3}}$.

$\text{Area} = \frac{h^2}{\sqrt{3}}$

Calculate the Area

Substitute $h = 6$ into the formula: $\text{Area} = \frac{6^2}{\sqrt{3}} = \frac{36}{\sqrt{3}}$. To rationalize, multiply the numerator and denominator by $\sqrt{3}$.

$\text{Area} = \frac{36}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{36\sqrt{3}}{3} = 12\sqrt{3}$