In the figure, how do I find the value of the variable? 
According to the problem, I have to find the value of the variable in simplest radical form. I began with the equation 18√9 = 6 (1/3)x, so x = 9√3. Now, I know we have to find the area of the base in terms of x. But how do I find the height; do I use Pythagorean Theorem? 

\begin{gathered}
V\ =\ \frac{Bh}{3} \ \ \ where\ B\ is\ the\ base\ area\ of\ the\ equilateral\ triangle\ of\ length\ x\\
\\
B\ =\ \frac{1}{2} \ ( base\ triangle\ length)( base\ triangle\ height) \ =\ \ \frac{1}{2} \ ( x)\left(\frac{\sqrt{3} x}{2} \ \right) \ =\ \frac{\sqrt{3} x^{2}}{4}\\
\\
V\ =\ \frac{1}{3} \ *\ \frac{\sqrt{3} x^{2}}{4} \ *\ 6\ \ =\ \frac{6\sqrt{3} x^{2}}{12} \ =\ \frac{\sqrt{3} x^{2}}{2}\\
\ \ \\
\ 18\sqrt{3} \ =\ \frac{\sqrt{3} x^{2}}{2}\\
\\
36\ =\ x^{2} \ \ \ \ \ \ \ \ \ so\ \ \ \ \ \ \ \ x\ =\ 6\\
\end{gathered}
