1. **State the problem:** Find the volume of the dollhouse, which consists of a rectangular prism base and a triangular prism roof. 2. **Formula for volume:** - Volume of rectangular prism: $$V_{rect} = l \times w \times h$$ - Volume of triangular prism: $$V_{tri} = \text{area of triangle} \times \text{length}$$ 3. **Calculate the volume of the rectangular prism base:** - Given dimensions: length $l = 2.1$ ft, width $w = 1.5$ ft, height $h = 0.6$ ft - $$V_{rect} = 2.1 \times 1.5 \times 0.6 = 1.89 \text{ ft}^3$$ 4. **Calculate the volume of the triangular prism roof:** - The triangular face has base $b = 1.2$ ft and height $h = 0.5$ ft - Area of triangle: $$A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 1.2 \times 0.5 = 0.3 \text{ ft}^2$$ - Length of the prism (same as width of base): $1.5$ ft - Volume of roof: $$V_{tri} = 0.3 \times 1.5 = 0.45 \text{ ft}^3$$ 5. **Add volumes to find total volume:** - $$V_{total} = V_{rect} + V_{tri} = 1.89 + 0.45 = 2.34 \text{ ft}^3$$ **Final answer:** The volume of the dollhouse is **2.34 cubic feet**.