The volume \( V \) of a rectangular prism can be calculated using the formula:
\[ V = \text{Base Area} \times \text{Height} \]
Given that the volume of the rectangular prism is 252 in³, we can denote the base area as \( A \) and the height as \( h \):
\[ A \times h = 252 \text{ in}^3 \]
For a rectangular pyramid with a base area and height congruent to that of the prism, the volume \( V \) of the pyramid is calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Substituting the base area \( A \) and height \( h \) from the prism's volume:
\[ V = \frac{1}{3} \times A \times h \]
Since we know that \( A \times h = 252 \text{ in}^3 \):
\[ V = \frac{1}{3} \times 252 \text{ in}^3 \]
Calculating this gives:
\[ V = \frac{252}{3} = 84 \text{ in}^3 \]
Thus, the volume of the pyramid is
\[ \boxed{84 \text{ in}^3} \]