1. **State the problem:** We need to find the area of the seating region, which is the ring-shaped sector between two concentric circles with radii 117 m and 23 m, both having a central angle of 75°. 2. **Formula for the area of a sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by $$A = \frac{\theta}{360} \times \pi r^2$$ 3. **Calculate the area of the larger sector (outer radius 117 m):** $$A_{outer} = \frac{75}{360} \times \pi \times 117^2$$ 4. **Calculate the area of the smaller sector (inner radius 23 m):** $$A_{inner} = \frac{75}{360} \times \pi \times 23^2$$ 5. **Find the area of the seating region by subtracting inner area from outer area:** $$A_{seating} = A_{outer} - A_{inner} = \frac{75}{360} \times \pi (117^2 - 23^2)$$ 6. **Simplify inside the parentheses:** $$117^2 = 13689, \quad 23^2 = 529$$ $$13689 - 529 = 13160$$ 7. **Substitute back:** $$A_{seating} = \frac{75}{360} \times \pi \times 13160$$ 8. **Simplify the fraction:** $$\frac{75}{360} = \frac{\cancel{75}}{\cancel{360}} = \frac{5}{24}$$ 9. **Final expression:** $$A_{seating} = \frac{5}{24} \times \pi \times 13160 = \frac{5 \times 13160}{24} \pi$$ 10. **Calculate the numeric value:** $$\frac{5 \times 13160}{24} = \frac{65800}{24} \approx 2741.6667$$ 11. **Multiply by $\pi$ and round to nearest tenth:** $$A_{seating} \approx 2741.6667 \times 3.1416 = 8607.5 \text{ m}^2$$ **Answer:** The area of the seating region is approximately **8607.5 m²**.