To find the area of the circle when the circumference is given, we can use the formulas for circumference and area of a circle.
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The formula for circumference \( C \) is: \[ C = 2\pi r \] where \( r \) is the radius.
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The formula for area \( A \) is: \[ A = \pi r^2 \]
Given that the circumference is 12, we can find the radius:
\[ 12 = 2\pi r \]
To solve for \( r \): \[ r = \frac{12}{2\pi} = \frac{6}{\pi} \]
Now we can find the area using the radius: \[ A = \pi r^2 = \pi \left(\frac{6}{\pi}\right)^2 = \pi \cdot \frac{36}{\pi^2} = \frac{36}{\pi} \]
Now we will calculate the area:
Using \(\pi \approx 3.14\): \[ A \approx \frac{36}{3.14} \approx 11.46 \]
Rounding to the nearest tenth, the area is approximately \( 11.5 \) square units.
However, looking at the given options, the closest match to our calculated area is:
11.46 sq units.
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