To find the area of the circle given its circumference, you can use the formulas for circumference and area. The circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius. The area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
Given that the circumference is 198 feet, you can solve for the radius:
\[ 198 = 2\pi r \]
To find \( r \):
\[ r = \frac{198}{2\pi} = \frac{99}{\pi} \]
Now, we can substitute \( r \) into the area formula:
\[ A = \pi r^2 = \pi \left(\frac{99}{\pi}\right)^2 \]
Simplifying this:
\[ A = \pi \cdot \frac{9801}{\pi^2} = \frac{9801}{\pi} \]
Next, to calculate the area, we can use \( \pi \approx 3.14 \):
\[ A \approx \frac{9801}{3.14} \approx 3120.06 \]
Rounding to the nearest square foot, the area is approximately:
\[ 3120 , \text{ft}^2 \]
Therefore, the correct answer is:
3,120 ft.²
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