To find the volume of the rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base of the pyramid is congruent to the base of the rectangular prism, and the height of the pyramid is the same as the height of the prism.
The volume of the rectangular prism is given as 252 cubic inches. The volume of a prism can be expressed as:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} \]
Since the base and height of the pyramid are the same as those of the prism, we have that:
\[ \text{Base Area} \times \text{Height} = 252 \]
Now, substituting this into the volume formula for the pyramid, we get:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 252 \]
Calculating this:
\[ V_{\text{pyramid}} = \frac{252}{3} = 84 \]
Thus, the volume of the rectangular pyramid is \( \boxed{84} \) cubic inches.