To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
We know the base area of the pyramid is 16 in², and we need to find the height (\(h\)). We also know that the volume of the prism does not directly affect the volume of the pyramid, but it may give us context.
To find the volume of the pyramid, we can set it equal to some volume \(V\) and solve for \(h\):
\[ V = \frac{1}{3} \times 16 , \text{in}^2 \times h \]
We can calculate the volume of a rectangular prism with the same base area given:
\[ \text{Volume of the rectangular prism} = \text{Base Area} \times \text{Height} = 288 , \text{in}^3 \]
Since the base area is the same for both the prism and the pyramid, we have:
\[ 288 = 16 \times \text{Height of the prism} \]
To find the height of the prism, we divide:
\[ \text{Height of the prism} = \frac{288}{16} = 18 , \text{in} \]
Now, let’s set the volume of the pyramid equal to 288 in³, assuming it reached the same volume to find the height of the pyramid:
\[ 288 = \frac{1}{3} \times 16 \times h \]
Now, solve for \(h\):
\[ 288 = \frac{16h}{3} \]
Multiply both sides by 3:
\[ 864 = 16h \]
Now divide by 16:
\[ h = \frac{864}{16} = 54 , \text{in} \]
Thus, the height of the rectangular pyramid is:
\[ \boxed{54 , \text{in.}} \]