The image shows a triangular prism, and we are asked to find its volume. The dimensions provided are:

• Height of the triangular face: 5 inches
• Base of the triangular face: 6 inches
• Length (depth) of the prism: 2 inches

The volume $V$ of a triangular prism is given by the formula:

$V = \text{Area of the triangular base} \times \text{Length (depth) of the prism}$

Step 1: Find the area of the triangular base

The area $A$ of a triangle is calculated as:

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

Using the given dimensions:

• Base = 6 inches
• Height = 5 inches

$A = \frac{1}{2} \times 6 \times 5 = 15 \, \text{square inches}$

Step 2: Calculate the volume of the prism

Now, multiply the area of the triangular base by the length of the prism (2 inches):

$V = 15 \times 2 = 30 \, \text{cubic inches}$

So, the volume of the prism is 30 cubic inches.

Would you like more details on this calculation or have any questions?

Here are 5 related questions to explore further:

1. What is the formula for the volume of other types of prisms?
2. How would the volume change if the length of the prism were doubled?
3. What are some real-life examples where triangular prisms are used?
4. How does the volume of a prism compare to the volume of a cylinder with the same base area?
5. What would happen if the height of the triangular base were increased?

Tip: For any prism, always remember that the volume is the product of the base area and the height (or length) of the prism.