To find the volume of the pyramid with the same triangular base and height as the prism, we need to use the formulas for the volumes of these shapes.
The volume \( V \) of a prism is calculated using the formula:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} \]
The volume \( V \) of a pyramid is calculated using the formula:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Since the prism and pyramid have the same base area and height, we can determine the volume of the pyramid in relation to the volume of the prism.
Given that the volume of the prism is 1,092 cubic units, we can set:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} = 1,092 \]
Now, to find the volume of the pyramid:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times V_{\text{prism}} \]
Substituting the volume of the prism:
\[ V_{\text{pyramid}} = \frac{1}{3} \times 1,092 = 364 \]
Therefore, the volume of the pyramid is:
\[ \boxed{364 \text{ cubic units}} \]