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

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

The given dimensions are:

• The base of the triangular prism: 9.8 in (height of the triangle)
• The base of the triangular face: 2.5 in (base of the triangle)
• The height (length) of the prism: 14 in

First, calculate the area of the triangular base:

$\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2.5 \times 9.8 = \frac{1}{2} \times 24.5 = 12.25 \text{ square inches}$

Next, calculate the volume of the prism:

$\text{Volume} = \text{Base Area} \times \text{Height} = 12.25 \times 14 = 171.5 \text{ cubic inches}$

Therefore, the volume of the triangular prism, rounded to the nearest tenth, is 171.5 cubic inches.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the volume change if the length of the prism were doubled?
2. Can you explain how to find the surface area of this triangular prism?
3. What is the formula for the volume of a prism with a different shaped base?
4. How would you determine the volume if the triangular base were equilateral?
5. What if the height of the triangle was incorrect, how would this affect the volume calculation?

Tip: Always double-check the units when calculating the volume to ensure consistency, particularly when combining measurements in different units.