1. **State the problem:** We need to find the area of a circular swimming pool with a diameter of 21 feet. 2. **Formula:** The area $A$ of a circle is given by the formula: $$A = \pi r^2$$ where $r$ is the radius of the circle. 3. **Find the radius:** The radius is half the diameter: $$r = \frac{21}{2} = 10.5 \text{ feet}$$ 4. **Calculate the area:** Substitute $r = 10.5$ into the area formula: $$A = \pi (10.5)^2 = \pi \times 110.25$$ 5. **Evaluate the area:** Using $\pi \approx 3.1416$, $$A \approx 3.1416 \times 110.25 = 346.36 \text{ square feet}$$ 6. **Final answer:** The area of the pool is approximately $$\boxed{346.4 \text{ square feet}}$$