1. **State the problem:** Calculate the volume of a 3D shape that consists of a rectangular base and a triangular prism roof. 2. **Identify the dimensions:** - Rectangular base: length $l = 4.5$ cm, width $w = 2$ cm, height $h_b = 3$ cm - Triangular prism roof: height of each triangular side $h_t = 3.5$ cm, vertical height from base to roof peak $h_r = 2$ cm 3. **Volume formula for the rectangular base:** $$V_{base} = l \times w \times h_b$$ 4. **Calculate the base volume:** $$V_{base} = 4.5 \times 2 \times 3 = 27 \text{ cm}^3$$ 5. **Volume formula for the triangular prism roof:** The triangular cross-section area is $$A_{triangle} = \frac{1}{2} \times \text{base of triangle} \times \text{height of triangle}$$ The base of the triangle is the width of the house $w = 2$ cm, and the height is the vertical height $h_r = 2$ cm. So, $$A_{triangle} = \frac{1}{2} \times 2 \times 2 = 2 \text{ cm}^2$$ The volume of the prism is the area of the triangle times the length of the house: $$V_{roof} = A_{triangle} \times l = 2 \times 4.5 = 9 \text{ cm}^3$$ 6. **Calculate total volume:** $$V_{total} = V_{base} + V_{roof} = 27 + 9 = 36 \text{ cm}^3$$ **Final answer:** The volume of the shape is $36$ cubic centimeters.