To determine whether a triangular prism is larger than a pyramid by three times, we need to compare their volumes. The volume of each shape can be calculated using specific formulas.
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Volume of a Triangular Prism: \[ V_{\text{prism}} = B \cdot h \] where \( B \) is the area of the triangular base and \( h \) is the height of the prism.
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Volume of a Pyramid: \[ V_{\text{pyramid}} = \frac{1}{3} B \cdot h \] where \( B \) is the area of the base (which can be a triangle, square, etc.) and \( h \) is the height of the pyramid.
If we assume that the triangular prism and the pyramid have the same base area \( B \) and the same height \( h \), we can plug in the values into the formulas:
For the prism: \[ V_{\text{prism}} = B \cdot h \]
For the pyramid: \[ V_{\text{pyramid}} = \frac{1}{3} B \cdot h \]
Now, we can compare the two volumes: \[ V_{\text{prism}} = 3 \cdot V_{\text{pyramid}} \]
Thus, the volume of the triangular prism is indeed 3 times the volume of the pyramid, assuming both shapes have the same base area and height.