Subjects geometry

Tent Volume 173E00

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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**.
4 m 3 m 10 m