To find the area of the pitcher's circle, we can use the formula for the area of a circle, which is given by:
\[ A = \pi r^2 \]
where \(A\) is the area and \(r\) is the radius of the circle.
Given that the diameter of the circle is 18 feet, we can find the radius by dividing the diameter by 2:
\[ r = \frac{diameter}{2} = \frac{18 \text{ feet}}{2} = 9 \text{ feet} \]
Now, we can plug the radius into the area formula:
\[ A = \pi (9 \text{ feet})^2 = \pi (81 \text{ square feet}) = 81\pi \text{ square feet} \]
Using the approximation \(\pi \approx 3.14\), we can also calculate the numerical area:
\[ A \approx 81 \times 3.14 \approx 254.34 \text{ square feet} \]
Therefore, the area of the pitcher's circle is approximately \(254.34\) square feet, or exactly \(81\pi\) square feet.