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

$\text{Volume} = \text{Base Area} \times \text{Height of the Prism}$

Step 1: Find the area of the triangular base

The area of a triangle is calculated as:

$\text{Area} = \frac{1}{2} \times \text{Base of the Triangle} \times \text{Height of the Triangle}$

From the diagram:

• Base of the triangle = $7 \, \text{cm}$
• Height of the triangle = $6 \, \text{cm}$

$\text{Area} = \frac{1}{2} \times 7 \times 6 = 21 \, \text{cm}^2$

Step 2: Multiply by the prism's height

The height of the prism (or the length of the prism) is $10 \, \text{cm}$. So:

$\text{Volume} = \text{Base Area} \times \text{Height of the Prism} = 21 \times 10 = 210 \, \text{cm}^3$

Final Answer:

The volume of the triangular prism is:

$\boxed{210 \, \text{cm}^3}$

Let me know if you'd like more details or have questions! Here are five related questions for you to explore:

1. What would the volume be if the prism's height were doubled?
2. How does the formula change if the base of the triangle is an equilateral triangle?
3. What are some practical applications of finding the volume of triangular prisms?
4. How would the volume be affected if only the height of the triangle were increased by 50%?
5. How can the dimensions be used to calculate the surface area of the prism?

Tip: Always double-check your units in volume calculations to ensure consistency!