To find the area of a circle when given the circumference \( C = 12\pi \), we can use the relationship between circumference and radius:
\[ C = 2\pi r \]
Setting the given circumference equal to this formula, we have:
\[ 12\pi = 2\pi r \]
Now, we can solve for \( r \):
\[ r = \frac{12\pi}{2\pi} = 6 \]
Now that we have the radius, we can calculate the area \( A \) of the circle using the formula:
\[ A = \pi r^2 \]
Substituting the radius:
\[ A = \pi (6^2) = \pi (36) = 36\pi \]
So, the area of the circle is:
\[ \boxed{36\pi} \]