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: Identify the dimensions

From the image:

• The base of the triangle is $6 \ \text{yd}$.
• The height of the triangle is $9 \ \text{yd}$.
• The length (or height of the prism) is $7 \ \text{yd}$.

Step 2: Calculate the area of the triangular base

The area of a triangle is: $\text{Area of the base} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area of the base} = \frac{1}{2} \times 6 \times 9 = \frac{1}{2} \times 54 = 27 \ \text{yd}^2$

Step 3: Calculate the volume

$\text{Volume} = \text{Base Area} \times \text{Height of the prism}$ $\text{Volume} = 27 \times 7 = 189 \ \text{yd}^3$

Final Answer

The volume of the triangular prism is 189 cubic yards (yd³).

Would you like a deeper explanation or any additional details?
Here are five related questions to expand your understanding:

1. How do you find the surface area of a triangular prism?
2. If the length of the prism was doubled, what would the new volume be?
3. How does the formula for the volume of a triangular prism differ from that of a rectangular prism?
4. What are the units for volume, and why are they cubic?
5. How would changing only the base of the triangle affect the volume?

Tip: Always ensure units are consistent before applying any geometric formula.