The volume of a rectangular prism is calculated using the formula:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} \]
The volume of a pyramid with a base congruent to that of the prism and the same height is given by:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Since the bases and heights are congruent, the base area and height for both volumes are the same.
Given that the volume of the prism is \(420 , \text{in}^3\):
\[ 420 , \text{in}^3 = \text{Base Area} \times \text{Height} \]
To find the volume of the pyramid, we can substitute in the formula for the pyramid's volume:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times V_{\text{prism}} = \frac{1}{3} \times 420 , \text{in}^3 \]
Calculating this gives:
\[ V_{\text{pyramid}} = \frac{420}{3} = 140 , \text{in}^3 \]
Therefore, the volume of the pyramid is
\[ \boxed{140 , \text{in}^3} \]