This problem involves finding the volume of a triangular prism.

Given information:

• The bases of the prism are equilateral triangles with side lengths of 4 inches.
• The height of the equilateral triangle is 3.5 inches.
• The height (or length) of the prism is 6 inches.

Volume of a prism formula:

The formula for the volume $V$ of a prism is: $V = \text{Area of the base} \times \text{Height of the prism}$

Step 1: Find the area of the equilateral triangle base.

The area $A$ of an equilateral triangle is given by the formula: $A = \frac{\sqrt{3}}{4} \times s^2$ where $s$ is the side length of the equilateral triangle.

Substituting $s = 4$ inches: $A = \frac{\sqrt{3}}{4} \times (4)^2 = \frac{\sqrt{3}}{4} \times 16 = 4\sqrt{3} \text{ square inches}$

Step 2: Calculate the volume.

Now, we multiply the area of the base by the height of the prism: $V = 4\sqrt{3} \times 6$ $V = 24\sqrt{3} \text{ cubic inches}$ Approximating $\sqrt{3} \approx 1.732$: $V \approx 24 \times 1.732 = 41.57 \text{ cubic inches}$

So, the volume of the prism is approximately 41.57 cubic inches.

Would you like a more detailed explanation of any step? Or do you have any other questions?

Related Questions:

1. How do you find the area of an equilateral triangle?
2. How do you calculate the height of a prism?
3. What is the formula for the volume of a pyramid and how does it differ from a prism?
4. How does the shape of the base affect the volume of a prism?
5. Can you find the volume of a prism with a square base? How?

Tip: When calculating the volume of a prism, make sure to first find the area of the base shape and then multiply it by the height of the prism.