1. **State the problem:** Calculate the volume of a 3D house-like figure composed of a rectangular prism base and a triangular prism roof. 2. **Identify the shapes and dimensions:** - Rectangular prism base: length $45$ cm, width $17$ cm, height $20$ cm. - Triangular prism roof: base area is the same as the rectangle base ($45 \times 17$), height of the triangle (roof height) is $18$ cm. 3. **Formula for volume:** - Volume of rectangular prism: $V_{rect} = \text{length} \times \text{width} \times \text{height}$ - Volume of triangular prism: $V_{tri} = \text{area of triangular base} \times \text{length}$ 4. **Calculate the volume of the rectangular prism base:** $$V_{rect} = 45 \times 17 \times 20 = 15300 \text{ cm}^3$$ 5. **Calculate the area of the triangular base:** The triangular base has base $17$ cm and height $18$ cm, so $$A_{tri} = \frac{1}{2} \times 17 \times 18 = \frac{1}{2} \times 306 = 153 \text{ cm}^2$$ 6. **Calculate the volume of the triangular prism roof:** The length of the prism is $45$ cm, so $$V_{tri} = 153 \times 45 = 6885 \text{ cm}^3$$ 7. **Calculate total volume:** $$V_{total} = V_{rect} + V_{tri} = 15300 + 6885 = 22185 \text{ cm}^3$$ **Important note:** Your mistake was using $45 \times 17 \times 18$ for the roof volume, which assumes the roof is a rectangular prism. Instead, the roof is a triangular prism, so you must use half the area of the triangle base times the length. **Final answer:** $$\boxed{22185 \text{ cm}^3}$$