1. **State the problem:** Calculate the total surface area of a roof shaped as a rectangular prism with dimensions length = 15 m and width = 10 m, plus two trapezoidal sections at each end with bases 10 m and 15 m, and height 4 m. 2. **Formula for surface area:** The total surface area is the sum of the rectangular section area and the areas of the two trapezoidal sections. 3. **Calculate the rectangular section area:** $$\text{Area}_{rect} = \text{length} \times \text{width} = 15 \times 10 = 150 \text{ m}^2$$ 4. **Calculate the area of one trapezoidal section:** The area of a trapezoid is given by: $$\text{Area}_{trap} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1 = 10$ m, $b_2 = 15$ m, and $h = 4$ m. Calculate: $$\text{Area}_{trap} = \frac{(10 + 15)}{2} \times 4 = \frac{25}{2} \times 4 = 12.5 \times 4 = 50 \text{ m}^2$$ 5. **Calculate total trapezoidal area for both ends:** $$2 \times 50 = 100 \text{ m}^2$$ 6. **Calculate total surface area of the roof:** $$\text{Total Area} = \text{Area}_{rect} + 2 \times \text{Area}_{trap} = 150 + 100 = 250 \text{ m}^2$$ **Final answer:** The total surface area of the roof is $250$ square meters.