The volume of a prism is calculated using the formula:
\[ \text{Volume of Prism} = \text{Base Area} \times \text{Height} \]
The volume of a pyramid is calculated using the formula:
\[ \text{Volume of Pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given that both the prism and the pyramid have the same triangular base and the same height, we can relate their volumes. If the volume of the prism is 1,092 cubic units:
\[ \text{Volume of Prism} = \text{Base Area} \times \text{Height} = 1,092 \]
For the pyramid, we know that:
\[ \text{Volume of Pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times \text{Volume of Prism} \]
Substituting the volume of the prism into the equation for the pyramid:
\[ \text{Volume of Pyramid} = \frac{1}{3} \times 1,092 = 364 \text{ cubic units} \]
Thus, the volume of the pyramid is 364 cubic units.