Area of a Circle – Exact Answer (d = 12 ft)

Explanation

Since the diameter is 12 feet, the radius is:

\[r = \frac{12}{2} = 6 \text{ ft}\]

\[A = \pi r^2\]

This is the formula for the area of a circle.

\[A = \pi(6)^2\]

Substitute 6 for \(r\).

\[= \pi(36) = 36\pi\]

Evaluate \(6^2 = 36\) and write with \(\pi\) last.

The exact area of the circle is \(36\pi\) ft².