Question

A triangular prism is shown below the base is a right triangle
7 cm
4 cm width
10 cm long
What is the volume of the triangular prism
_____ cubic centimeters

Answer 1

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

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

In this case, the base of the triangular prism is a right triangle with one leg measuring 4 cm and the other leg measuring 7 cm. The height (or length) of the prism is given as 10 cm.

First, we need to calculate the area of the right triangle base:

\[
\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \, \text{cm} \times 7 \, \text{cm}
\]

Calculating that:

\[
\text{Base Area} = \frac{1}{2} \times 4 \times 7 = \frac{28}{2} = 14 \, \text{cm}^2
\]

Next, we can find the volume of the prism by multiplying the area of the base by the height (length of the prism):

\[
\text{Volume} = \text{Base Area} \times \text{Height} = 14 \, \text{cm}^2 \times 10 \, \text{cm}
\]

Calculating the volume:

\[
\text{Volume} = 140 \, \text{cm}^3
\]

Thus, the volume of the triangular prism is:

\[
\boxed{140} \text{ cubic centimeters}
\]