To find the volume of a pyramid with a square base, we'll use the volume formula for a pyramid, which is given by:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
Here, the base of the pyramid is a square with edge length [tex]\( n \)[/tex] units, so the area of the base [tex]\( A \)[/tex] is:
[tex]\[
\text{Base Area} = n^2 \text{ square units}
\][/tex]
The height [tex]\( h \)[/tex] of the pyramid is given as [tex]\( n - 1 \)[/tex] units.
Substituting these values into the volume formula, we get:
[tex]\[
V = \frac{1}{3} \times n^2 \times (n - 1)
\][/tex]
Simplifying this expression, we get:
[tex]\[
V = \frac{1}{3} n^2 (n - 1)
\][/tex]
This expression [tex]\( \frac{1}{3} n^2 (n - 1) \)[/tex] represents the volume of the pyramid.
So the correct choice among the given options is:
[tex]\[
\frac{1}{3} n^2 (n - 1) \text{ units}^3
\][/tex]
This precisely represents the volume of the pyramid with a square base edge length [tex]\( n \)[/tex] and height [tex]\( n - 1 \)[/tex].
