This is a triangular prism, and the volume of a triangular prism is calculated using the formula:

$V = \text{Base Area} \times \text{Height}$

Where:

• The base area is the area of the triangular cross-section.
• The height is the length of the prism (the distance between the two triangular faces).

From the image, the dimensions provided are:

• Base = 14 units
• Height of the triangle (perpendicular to the base) = 6 units
• Length of the prism = 17 units

Step 1: Calculate the area of the triangle (base area):

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

$A = \frac{1}{2} \times \text{Base} \times \text{Height}$

Substitute the values:

$A = \frac{1}{2} \times 14 \times 6 = 42 \, \text{square units}$

Step 2: Calculate the volume of the prism:

Now, use the formula for the volume:

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

Substitute the values:

$V = 42 \times 17 = 714 \, \text{cubic units}$

Thus, the volume of the prism is 714 cubic units.

Do you need any further explanation or details?

Here are some related questions to explore:

1. How would the volume change if the length of the prism were increased or decreased?
2. What would the volume be if the base of the triangle were changed to a different value?
3. How do you calculate the volume of a rectangular prism?
4. What are other types of prisms, and how are their volumes calculated?
5. Can the same formula be applied to other shapes such as pyramids?

Tip: Remember that for prisms, the cross-sectional area remains the same throughout the length of the prism!