1. **Stating the problem:** We need to find the total surface area of the composite 3D solid shown, which consists of a rectangular prism with a slanted roof. 2. **Understanding the shape and given dimensions:** - Base rectangle AB = 10 cm (length) - Depth BC = 8 cm (width) - Left vertical height AE = 9 cm - Right vertical height CG = 6 cm 3. **Formula for surface area of composite solids:** The total surface area is the sum of the areas of all visible faces. 4. **Calculate the areas of each face:** - Bottom face ABCD (rectangle): $$10 \times 8 = 80 \text{ cm}^2$$ - Left vertical face ABEF (rectangle): $$10 \times 9 = 90 \text{ cm}^2$$ - Right vertical face BCGF (trapezoid with heights 9 cm and 6 cm): Since the right side is slanted, the face BCGF is a trapezoid with bases 9 cm and 6 cm and height 8 cm. Area: $$\frac{(9 + 6)}{2} \times 8 = \frac{15}{2} \times 8 = 7.5 \times 8 = 60 \text{ cm}^2$$ - Back face DCGH (rectangle): $$10 \times 6 = 60 \text{ cm}^2$$ - Roof face EFJI (trapezoid): The roof is slanted with edges EF and IJ. The height difference is 3 cm (9 - 6). The length of the roof along EF is 10 cm. Area: $$\frac{(9 + 6)}{2} \times 10 = 7.5 \times 10 = 75 \text{ cm}^2$$ 5. **Sum all areas:** $$80 + 90 + 60 + 60 + 75 = 365 \text{ cm}^2$$ 6. **Final answer:** The total surface area of the composite solid is $$\boxed{365 \text{ cm}^2}$$