Question

What is the volume of this triangular right prism? (6 ft, 5 ft, 11 ft, 6.5 ft)

A. 165 ft^{3}
B. 330 ft^{3}
C. 1,073ft^{3}
D. 2,145ft^{3}

Answer 1

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

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

1. **Identify the Base Area:**

The triangular base can be determined since it forms a right triangle. The base and height of the triangle are the two legs of the right triangle, which are given as 6 ft and 5 ft.

The area \( A \) of a right triangle is given by the formula:

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

Thus, plugging in the values:

\[
A = \frac{1}{2} \times 6 \, \text{ft} \times 5 \, \text{ft} = \frac{1}{2} \times 30 \, \text{ft}^2 = 15 \, \text{ft}^2
\]

2. **Identify the Height of the Prism:**

The height \( h \) of the prism is given as 11 ft.

3. **Calculate the Volume:**

Now, substitute the base area and height into the volume formula:

\[
\text{Volume} = \text{Base Area} \times \text{Height} = 15 \, \text{ft}^2 \times 11 \, \text{ft} = 165 \, \text{ft}^3
\]

Therefore, the volume of the triangular right prism is:

\[
\boxed{165 \, \text{ft}^3}
\]

This corresponds to option A.