geometry question

Recall that a circle's radius can be found with the circumference using the formula $2 \pi r = 18 \pi$.

Solving for r, we find the circle's radius is 9. 

Now, remember that a triangle's circumradius is defined by the formula $abc \over 4 \times \text{Area}$. 

However, we have an equilateral triangle, so we have: $\large{s^3 \over { 4 \times {\sqrt 3 \over 4}s^2}} = 9$.

This equation simplifies to ${s \over \sqrt 3 } = 9$, meaning the side length of the triangle is $9 \sqrt 3$

Now, using the formula for the area of an equilateral triangle, we have: $(9 \sqrt3)^2 \times {\sqrt 3 \over 4} = \color{brown}\boxed{243 \sqrt 3 \over 4}$