To find the area of the circle given the circumference \( C = 12\pi \), we first need to use the formula for the circumference of a circle:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle. Setting the given circumference equal to this formula, we have:
\[ 12\pi = 2\pi r \]
Now we can solve for \( r \):
\[ r = \frac{12\pi}{2\pi} = 6 \]
Next, we can find the area \( A \) of the circle using the formula for area:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi (6)^2 = \pi \cdot 36 = 36\pi \]
Thus, the area of the circle is:
\[ \text{Area} = 36\pi \]
So the correct response is 36π.