To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid, which is:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
We know the base area is \( 16 , \text{in}^2 \), but we need to find the height (\( h \)) of the pyramid.
We also know that the volume of the rectangular prism is \( 288 , \text{in}^3 \). The volume of a rectangular prism is given by:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
However, since we are calculating the pyramid's height, we will use the volume of the pyramid and set it equal to \( 288 , \text{in}^3 \):
\[ 288 = \frac{1}{3} \times 16 \times h \]
Now, multiply both sides by 3 to eliminate the fraction:
\[ 864 = 16 \times h \]
Now, divide both sides by 16 to isolate \( h \):
\[ h = \frac{864}{16} \]
Performing the division:
\[ h = 54 \]
Thus, the height of the rectangular pyramid is \( 54 , \text{in} \).
The answer is 54 in.