1. **Stating the problem:** We need to find the volume of a festival tent shaped like a triangular prism. The tent has a triangular cross-section with a base width of 4 metres and a height of 3 metres, and the prism length is 10 metres.
2. **Formula for volume of a prism:** The volume $V$ of a prism is given by the formula:
$$V = \text{Area of cross-section} \times \text{length}$$
3. **Area of the triangular cross-section:** The area $A$ of a triangle is:
$$A = \frac{1}{2} \times \text{base} \times \text{height}$$
4. **Calculate the area:**
$$A = \frac{1}{2} \times 4 \times 3 = \frac{1}{2} \times 12 = 6$$ square metres.
5. **Calculate the volume:**
$$V = A \times \text{length} = 6 \times 10 = 60$$ cubic metres.
6. **Final answer:** The volume of the tent is **60 cubic metres**.
Tent Volume 173E00
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.