To find the volume of the triangular prism, we use the formula for the volume of a prism:

$V = \text{Base Area} \times \text{Height (Length of the prism)}$

Step 1: Find the area of the triangular base

The triangular base has a height of 8 meters and a base of 6 meters, as shown in the diagram. The formula for the area of a triangle is:

$A = \frac{1}{2} \times \text{Base} \times \text{Height}$

Substituting the given values:

$A = \frac{1}{2} \times 6 \, \text{m} \times 8 \, \text{m} = 24 \, \text{m}^2$

Step 2: Multiply the base area by the length of the prism

The length of the prism is 9 meters. Using the volume formula:

$V = 24 \, \text{m}^2 \times 9 \, \text{m} = 216 \, \text{m}^3$

Thus, the volume of the triangular prism is 216 cubic meters.

Do you need more details or have any questions?

Follow-up Questions:

1. How do we find the surface area of this triangular prism?
2. What happens to the volume if we double the length of the prism?
3. How can we calculate the perimeter of the triangular base?
4. What is the relationship between the base area and the volume of the prism?
5. Can we use the same formula for all types of prisms?

Tip:

Always ensure the units are consistent when calculating volume; the result should be in cubic units (e.g., cubic meters).