1. **State the problem:** We have two concentric circles (same center). The inner circle has diameter $d=51.8$ miles, and the outer circle has radius $r=13.2$ miles. We need to find the area of the shaded region between the two circles. 2. **Formula used:** The area of a circle is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Important rules:** - The shaded area between two concentric circles is the difference of their areas. - Radius is half the diameter. 4. **Calculate the radius of the inner circle:** $$r_{inner} = \frac{d}{2} = \frac{51.8}{2} = 25.9$$ miles 5. **Calculate the area of the inner circle:** $$A_{inner} = \pi (25.9)^2 = \pi \times 670.81 = 2106.19$$ square miles (rounded to 2 decimals) 6. **Calculate the area of the outer circle:** $$A_{outer} = \pi (13.2)^2 = \pi \times 174.24 = 547.77$$ square miles (rounded to 2 decimals) 7. **Find the shaded area (area between the two circles):** $$A_{shaded} = A_{inner} - A_{outer} = 2106.19 - 547.77 = 1558.42$$ square miles 8. **Final answer:** The area of the shaded region is **1558.42** square miles.