To find the area of the circle given the circumference \( C = 12\pi \), we can use the formulas for circumference and area of a circle.
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The formula for the circumference of a circle is given by: \[ C = 2\pi r \] where \( r \) is the radius.
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We can set \( 2\pi r \) equal to \( 12\pi \) and solve for the radius \( r \): \[ 2\pi r = 12\pi \] Dividing both sides by \( 2\pi \), we get: \[ r = \frac{12\pi}{2\pi} = 6 \]
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Next, we use the formula for the area \( A \) of a circle: \[ A = \pi r^2 \] Substituting \( r = 6 \): \[ A = \pi (6^2) = \pi \times 36 = 36\pi \]
Therefore, the area of the circle is \( \boxed{36\pi} \).