1. **State the problem:** We need to find the total surface area of the roof, which is a pentagonal prism shape with given side lengths 4.7 ft, 7.6 ft, 7.6 ft, 12 ft, and 18 ft. 2. **Understand the shape:** The roof is a pentagonal prism, so its surface area includes the areas of the two pentagonal bases and the rectangular faces connecting them. 3. **Calculate the area of the pentagonal base:** Since the base is irregular, we can split it into simpler shapes or use the given side lengths to find the area. However, the problem likely expects the surface area of the roof surface only, which is the two sloped rectangular faces (7.6 ft by 18 ft each) and the two triangular faces (formed by 4.7 ft, 7.6 ft, and 12 ft sides). 4. **Calculate the area of the two rectangular faces:** Each rectangle has dimensions 7.6 ft by 18 ft. $$\text{Area}_{rectangles} = 2 \times 7.6 \times 18 = 2 \times 136.8 = 273.6\, \text{ft}^2$$ 5. **Calculate the area of the two triangular faces:** Each triangle has base 12 ft and height 4.7 ft. $$\text{Area}_{triangles} = 2 \times \frac{1}{2} \times 12 \times 4.7 = 2 \times 28.2 = 56.4\, \text{ft}^2$$ 6. **Add the areas to find total roof surface area:** $$\text{Total area} = 273.6 + 56.4 = 330\, \text{ft}^2$$ 7. **Answer:** The builder needs **330 ft\textsuperscript{2}** of plywood to cover the entire roof surface.