To find the area of the circle given the circumference, we can follow these steps:
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Write the formula for circumference:
\[ C = 2\pi r \]
where \( C \) is the circumference and \( r \) is the radius.
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Substitute the given value of circumference:
\[ 22x = 2\pi r \]
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Solve for the radius \( r \):
\[ r = \frac{22x}{2\pi} = \frac{22x}{2 \times 3.14} = \frac{22x}{6.28} \]
Simplifying this gives:
\[ r = \frac{11x}{3.14} \]
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Write the formula for area:
\[ A = \pi r^2 \]
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Substitute the value of \( r \) into the area formula:
\[ A = \pi \left(\frac{11x}{3.14}\right)^2 \]
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Calculate \( r^2 \):
\[ r^2 = \left(\frac{11x}{3.14}\right)^2 = \frac{121x^2}{9.8596} \]
(where \( 9.8596 = 3.14^2\))
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Now substitute this back into the area formula:
\[ A = \pi \cdot \frac{121x^2}{9.8596} \]
Substituting \( \pi = 3.14 \):
\[ A = 3.14 \cdot \frac{121x^2}{9.8596} \]
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Calculate the area:
First, calculate \( 3.14 \times 121 \):
\[ 3.14 \times 121 = 379.94 \]
Now, divide by \( 9.8596 \):
\[ A = \frac{379.94x^2}{9.8596} \approx 38.49x^2 \]
Therefore, the area of the circle is approximately:
\[ \boxed{38.49x^2} \text{ square inches} \]