This image depicts a triangular prism with the given dimensions:

• Height of the triangular face: $9 \, \text{m}$
• Base of the triangular face: $7 \, \text{m}$
• Length (depth) of the prism: $4 \, \text{m}$

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

$\text{Volume} = \text{Base Area} \times \text{Length}$

Where:

• The base area is the area of the triangular face, which is calculated by:

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

Step-by-step calculation:

1. Base Area of the triangle: $\text{Base Area} = \frac{1}{2} \times 7 \, \text{m} \times 9 \, \text{m} = 31.5 \, \text{m}^2$

2. Volume of the prism: $\text{Volume} = 31.5 \, \text{m}^2 \times 4 \, \text{m} = 126 \, \text{m}^3$

Thus, the volume of the triangular prism is 126 cubic meters.

Would you like more details or have any other questions?

Here are 5 related questions:

1. How do you calculate the surface area of a triangular prism?
2. What is the formula for the volume of other types of prisms?
3. How do you find the volume of a pyramid?
4. What is the relationship between surface area and volume for prisms?
5. Can the volume formula change for prisms with different base shapes?

Tip: For any prism, the volume is always the area of the base times the height (or length).