To calculate the area of a circle, we use the formula:
\[ A = \pi \times r^2 \]
where \( r \) is the radius of the circle. Given that the diameter is 13 inches, we can find the radius \( r \) by dividing the diameter by 2:
\[ r = \frac{13}{2} = 6.5 \text{ inches} \]
Now, we can substitute the radius into the area formula:
\[ A = 3.14 \times (6.5)^2 \]
First, calculate \( (6.5)^2 \):
\[ (6.5)^2 = 42.25 \]
Now, plug this value into the area formula:
\[ A = 3.14 \times 42.25 \]
Calculating this gives:
\[ A \approx 133.455 \]
Now, round to the nearest hundredth:
\[ A \approx 133.46 \text{ in}^2 \]
Thus, the area of the circle is approximately:
\[ \boxed{133.46} \text{ in}^2 \]