1. **State the problem:** Calculate the surface area of a right prism with a trapezoidal roof. 2. **Identify dimensions:** - Base rectangle: length $= 16$ cm, width $= 5$ cm - Prism height (depth): $= 9$ cm - Roof slant height: $= 6$ cm - Roof slant diagonal length: $= 10$ cm 3. **Calculate the area of the rectangular base:** $$\text{Base area} = 16 \times 5 = 80 \text{ cm}^2$$ 4. **Calculate the area of the rectangular vertical faces:** - Front and back faces: $9 \times 16 = 144$ cm² each - Left and right faces: $9 \times 5 = 45$ cm² each Total vertical faces area: $$2 \times 144 + 2 \times 45 = 288 + 90 = 378 \text{ cm}^2$$ 5. **Calculate the area of the trapezoidal roof:** - The trapezoidal face is formed by a base of 16 cm and an upper slant edge of 10 cm with vertical height $=6$ cm. - Area of trapezoid: $$\frac{1}{2} (16 + 10) \times 6 = \frac{1}{2} \times 26 \times 6 = 78 \text{ cm}^2$$ - Roof extends over the prism length 16 cm, so total roof area: $$78 \times 16 = 1248 \text{ cm}^2$$ 6. **Sum all areas for total surface area:** $$\text{Surface area} = \text{Base} + \text{Vertical faces} + \text{Roof} = 80 + 378 + 1248 = 1706 \text{ cm}^2$$ **Final answer:** The surface area of the prism is $\boxed{1706 \text{ cm}^2}$.