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

$\text{Volume} = \text{Area of triangular base} \times \text{Length}$

Step 1: Calculate the area of the triangular base

The triangle in the cross-section has a base of $2.2 \, \text{m}$ and a height of $1.7 \, \text{m}$. The formula for the area of a triangle is:

$\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$

Substituting the values:

$\text{Area} = \frac{1}{2} \times 2.2 \, \text{m} \times 1.7 \, \text{m}$

$\text{Area} = \frac{1}{2} \times 3.74 \, \text{m}^2 = 1.87 \, \text{m}^2$

Step 2: Calculate the volume of the prism

The length of the prism is $3 \, \text{m}$. Using the formula for the volume:

$\text{Volume} = \text{Area of base} \times \text{Length} = 1.87 \, \text{m}^2 \times 3 \, \text{m}$

$\text{Volume} = 5.61 \, \text{m}^3$

Final Answer:

The volume of the triangular prism is approximately $5.6 \, \text{m}^3$ (to 1 decimal place).

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How would the volume change if the length of the prism doubled?
2. What is the volume if the height of the triangle increased to 2 m?
3. How would you calculate the surface area of this triangular prism?
4. What formula would you use if the prism had a circular cross-section?
5. Can this formula apply to prisms with non-triangular bases?

Tip: Always remember that volume units are cubic (e.g., $\text{m}^3$) since they represent 3-dimensional space.