To calculate the volume of the triangular prism, we follow these steps:

Step 1: Identify the components

The volume $V$ of a triangular prism is given by the formula: $V = \text{Base Area} \times \text{Height of the prism}$

Base Area:

The base of the triangular prism is a triangle. The area $A$ of a triangle is: $A = \frac{1}{2} \times \text{Base of the triangle} \times \text{Height of the triangle}$

From the diagram:

• The base of the triangle = $8 \, \text{cm}$
• The height of the triangle = $6 \, \text{cm}$

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

Height of the prism:

The length of the prism (depth) is $9 \, \text{cm}$.

Step 2: Calculate the volume

Substituting the values into the volume formula: $V = \text{Base Area} \times \text{Height of the prism} = 24 \times 9 = 216 \, \text{cm}^3$

Final Answer:

The volume of the triangular prism is: $\boxed{216 \, \text{cm}^3}$

Would you like further clarification or additional examples?

Here are 5 related questions you might find interesting:

1. How do you find the surface area of this triangular prism?
2. What happens to the volume if the base of the triangle is doubled?
3. Can you derive the volume formula for a cylinder and compare it with that of a prism?
4. How does the volume change if the height of the triangle and the prism are both halved?
5. What are some practical applications of triangular prisms in real life?

Tip: Always double-check your measurements to ensure accuracy, especially when dealing with composite shapes.