1. **State the problem:** We need to find the volume of a 3D house-shaped figure composed of a rectangular base and a triangular prism roof. 2. **Identify the shapes and dimensions:** - Rectangular base dimensions: length = 4.5 cm, width = 3 cm, height = 2 cm - Triangular prism roof with triangular base edges 3.5 cm, height of the triangle (roof height) = 2 cm 3. **Volume of the rectangular base:** The volume formula for a rectangular prism is: $$V_{base} = \text{length} \times \text{width} \times \text{height}$$ Substitute the values: $$V_{base} = 4.5 \times 3 \times 2 = 27 \text{ cm}^3$$ 4. **Volume of the triangular prism roof:** First, find the area of the triangular base of the prism. The triangle has base = 4.5 cm (same as the length of the base) and height = 2 cm (given roof height). Area of triangle: $$A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4.5 \times 2 = 4.5 \text{ cm}^2$$ The length (depth) of the prism is the width of the base = 3 cm. Volume of triangular prism: $$V_{roof} = A \times \text{length} = 4.5 \times 3 = 13.5 \text{ cm}^3$$ 5. **Total volume of the house-shaped figure:** $$V_{total} = V_{base} + V_{roof} = 27 + 13.5 = 40.5 \text{ cm}^3$$ **Final answer:** The volume of the house-shaped figure is **40.5 cm³**.