Final answer:
The volume of the triangular prism is calculated using the area of the triangular base times the height of the prism. For a prism with base sides of 4m and 7m and a height of 8m, the volume is 112 cubic meters (112m³).
Step-by-step explanation:
To calculate the volume of a triangular prism, you need to find the area of the base triangle and then multiply it by the height (length) of the prism. The formula for the volume of the prism is V = B × h, where V represents the volume, B is the area of the triangular base, and h is the height of the prism. If we assume that the measurements provided (4m, 7m, 8m) correspond to the height of the prism and the two sides of the right-angled base, then we could calculate the area of the base triangle using the formula for a right-angled triangle, which is A = \(rac{1}{2}\) × base × height. In our case, the base can be taken as 4m and height as 7m.
Steps to calculate the volume:
- Calculate the base area:
A = \(rac{1}{2}\) × 4m × 7m = \(rac{1}{2}\) × 28m² = 14m². - Multiply the area of the base by the height (length) of the prism:
V = 14m² × 8m = 112m³.
Hence, the volume of the triangular prism is 112 cubic meters (112m³).