Question

If h = 6 units, X = 7 units, Y = 6 units, and Z = 16 units, what is the volume of the triangular prism shown above?
A.
576 cubic units
B.
288 cubic units
C.
336 cubic units
D.
356 cubic units

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, \( h = 6 \) units is the height of the prism. To find the base area, we need to determine the area of the triangle with the dimensions given. The base and height of the triangle can be derived from the values of \( X \), \( Y \), and \( Z \), but we usually assume \( Z \) is the base for a triangular cross-section.

Let's say the triangular base has a base \( b \) (which we can take to be \( Z = 16 \) units) and a height \( h \) (which we can take to be the height of the triangle, given as \( Y = 6 \) units or independent height).

The area \( A \) of the triangle can be calculated as:

\[
A = \frac{1}{2} \times b \times h
\]

Here we try to determine if we have the correct triangle dimensions. If we use \( b = Z = 16 \) units and \( h = Y = 6 \) units:
Then the area will be:

\[
A = \frac{1}{2} \times 16 \times 6
\]

Calculating this gives:

\[
A = \frac{1}{2} \times 96 = 48 \text{ square units}
\]

Now, we multiply the area of the triangular base by the height of the prism:

\[
\text{Volume} = A \times h = 48 \times 7 = 336 \text{ cubic units}
\]

Thus, the volume of the triangular prism is \( \boxed{336} \) cubic units, which corresponds to option C.