Identify the relationship between altitude and side

In an equilateral triangle with side length 'a', the altitude 'h' is related to 'a' by the formula $h = \frac{\sqrt{3}}{2}a$. Thus, $a = \frac{2h}{\sqrt{3}}$.

$a = \frac{2 \times 9}{\sqrt{3}} = \frac{18}{\sqrt{3}}$

Calculate the area using the standard formula

The area of an equilateral triangle is $\frac{\sqrt{3}}{4}a^2$. Substituting $a = \frac{18}{\sqrt{3}}$ gives: $\text{Area} = \frac{\sqrt{3}}{4} \times (\frac{18}{\sqrt{3}})^2$.

$\text{Area} = \frac{\sqrt{3}}{4} \times \frac{324}{3} = \frac{\sqrt{3}}{4} \times 108 = 27\sqrt{3}$

Final Verification

The calculated area is $27\sqrt{3}cm^2$, which matches option D.

$\text{Area} = 27\sqrt{3}$