Question

What is the volume of this solid?

A triangular prism. The triangular base has a base of 10 inches and height of 7 inches. The height of the prism is 8 inches.

Recall the formula V = Bh.
280 cubic inches
385 cubic inches
465 cubic inches
560 cubic inches

Answer 1

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

\[
V = B \times h
\]

where \( V \) is the volume, \( B \) is the area of the triangular base, and \( h \) is the height of the prism.

1. **Calculate the area of the triangular base (B)**:
The area \( A \) of a triangle can be calculated with the formula:

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

For this triangle, the base is 10 inches and the height is 7 inches:

\[
A = \frac{1}{2} \times 10 \times 7 = \frac{1}{2} \times 70 = 35 \text{ square inches}
\]

2. **Calculate the volume of the prism (V)**:
Now, using the height of the prism, which is 8 inches:

\[
V = B \times h = 35 \times 8 = 280 \text{ cubic inches}
\]

Thus, the volume of the solid (triangular prism) is

\[
\boxed{280 \text{ cubic inches}}.
\]