1. **State the problem:** We need to find how many 4 feet by 9 feet panels are required to cover the outside perimeter of the structure. 2. **Identify the total perimeter length:** From the given data, the total horizontal length at the bottom is 63 feet, and other lengths include 216 feet and 18 feet for a rectangular section. The curved segment has radius $R=9$ feet and central angle $270^\circ$. 3. **Calculate the length of the curved segment:** The arc length $L$ of a circle segment is given by $$L = 2\pi R \times \frac{\theta}{360^\circ}$$ where $\theta = 270^\circ$ and $R=9$ feet. Calculate: $$L = 2 \pi \times 9 \times \frac{270}{360} = 18\pi \times \frac{3}{4} = 13.5\pi \approx 42.41 \text{ feet}$$ 4. **Calculate total perimeter length:** Add the straight lengths and the curved length. Given the rectangular section is $216$ ft by $18$ ft, perimeter of rectangle is $2(216 + 18) = 468$ ft. Adding the curved segment length: $$\text{Total perimeter} = 468 + 42.41 = 510.41 \text{ feet}$$ 5. **Calculate area to cover:** Since panels cover the outside, assume the height is 9 feet (panel height). The total area to cover is perimeter times height: $$\text{Area} = 510.41 \times 9 = 4593.69 \text{ square feet}$$ 6. **Calculate area of one panel:** Each panel is 4 ft by 9 ft, so $$\text{Panel area} = 4 \times 9 = 36 \text{ square feet}$$ 7. **Calculate number of panels needed:** $$\text{Number of panels} = \frac{4593.69}{36} \approx 127.6$$ Since panels must be whole, round up: $$\boxed{128 \text{ panels}}$$ **Final answer:** It takes 128 panels of size 4 feet by 9 feet to cover the outside of the structure.