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

$V = B \cdot h$

where:

• $B$ is the area of the triangular base.
• $h$ is the height (or length) of the prism, which is 32 cm in this case.

Step 1: Calculate the Area of the Triangular Base

The base is a right triangle with dimensions:

• Height of the triangle = 6 cm
• Base of the triangle = 9 cm

The area $B$ of a triangle is given by:

$B = \frac{1}{2} \times \text{base} \times \text{height}$

Substitute the values:

$B = \frac{1}{2} \times 9 \times 6 = \frac{1}{2} \times 54 = 27 \text{ cm}^2$

Step 2: Calculate the Volume of the Prism

Now, use the volume formula $V = B \cdot h$:

$V = 27 \times 32 = 864 \text{ cm}^3$

Answer

The volume of the triangular prism is:

$\boxed{864 \text{ cm}^3}$

Let me know if you'd like more details or have questions. Here are five related questions for further practice:

1. How would the volume change if the length of the prism were doubled?
2. What would be the volume if the triangular base dimensions were halved?
3. How can you calculate the surface area of this triangular prism?
4. If the height of the triangular base was 8 cm instead of 6 cm, what would be the new volume?
5. How would you calculate the volume if the base was not a right triangle?

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