What is the volume of this triangular prism?

A triangular prism has length 16 feet, width 4 feet and height 9 feet.

576 ft^3

288 ft^3

34 ft^3

29 ft^3

1 answer

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

\[ \text{Volume} = \text{Base Area} \times \text{Length} \]

For a triangular prism, the base area is given by the formula for the area of a triangle:

\[ \text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

In this case, we have:

  • Base (width) = 4 feet
  • Height of the triangle = 9 feet
  • Length of the prism = 16 feet

First, calculate the base area:

\[ \text{Base Area} = \frac{1}{2} \times 4 , \text{ft} \times 9 , \text{ft} = \frac{1}{2} \times 36 , \text{ft}^2 = 18 , \text{ft}^2 \]

Now, calculate the volume of the prism:

\[ \text{Volume} = 18 , \text{ft}^2 \times 16 , \text{ft} = 288 , \text{ft}^3 \]

Thus, the volume of the triangular prism is \( \boxed{288 , \text{ft}^3} \).