To find the volume of a pyramid that has the same triangular base and height as a prism with a volume of 1,092 cubic units, we can use the fact that the volume of a pyramid is one-third of the volume of a prism with the same base area and height.
The formula for the volume of a prism is given by:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} \]
And the formula for the volume of a pyramid is:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Since the height of both the prism and the pyramid is the same and the base area is the same, we can express the volume of the pyramid in terms of the volume of the prism:
\[ V_{\text{pyramid}} = \frac{1}{3} V_{\text{prism}} \]
Given that the volume of the prism \(V_{\text{prism}} = 1,092\) cubic units, we can substitute this value into the equation:
\[ V_{\text{pyramid}} = \frac{1}{3} \times 1,092 \]
Calculating this gives:
\[ V_{\text{pyramid}} = 364 \text{ cubic units} \]
Therefore, the volume of the pyramid is 364 cubic units.