1. **Problem statement:** The light on a lighthouse can reach a maximum distance of 20 miles and rotates 360 degrees. We need to find the total area illuminated by the light. 2. **Formula used:** The area illuminated by the light is the area of a circle with radius equal to the maximum distance the light can reach. The formula for the area of a circle is: $$A = \pi r^2$$ where $r$ is the radius. 3. **Substitute the given radius:** $$A = \pi \times 20^2$$ 4. **Calculate the square:** $$20^2 = 400$$ 5. **Calculate the area:** $$A = \pi \times 400 = 400\pi$$ 6. **Approximate the value:** Using $\pi \approx 3.1416$, $$A \approx 400 \times 3.1416 = 1256.64$$ **Final answer:** The total area that the lighthouse light can illuminate is approximately $1256.64$ square miles.