The circumference of a circle is \( 12 \pi \mathrm{ft} \). What is the area, in square feet? Express your answer in terms of \( \pi \).

To find the area of the circle, we first need to determine its radius from the given circumference. The formula for the circumference \( C \) of a circle is: \[ C = 2\pi r \] where \( r \) is the radius. We have \( C = 12\pi \). Setting the two expressions for circumference equal gives us: \[ 2\pi r = 12\pi \] Dividing both sides by \( 2\pi \): \[ r = \frac{12\pi}{2\pi} = 6 \text{ ft} \] Now, to find the area \( A \) of the circle, we use the formula: \[ A = \pi r^2 \] Substituting the radius: \[ A = \pi (6)^2 = \pi \cdot 36 = 36\pi \] Thus, the area of the circle is \( 36\pi \) square feet.