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The base area of a pentagonal prism is given as 39.1 square units and its volume is given as 273.7 cubic units. It is required to find the height.
Recall that the volume of a prism with base area B and height h is given as:
[tex]V=B\cdot h[/tex]Substitute V=273.7 and B=39.1 into the formula and solve for h:
[tex]\begin{gathered} 273.7=39.1\cdot h \\ \text{ Divide both sides by }39.1: \\ \Rightarrow\frac{273.7}{39.1}=\frac{39.1\cdot h}{39.1} \\ \Rightarrow7=h \end{gathered}[/tex]Hence, the height of the pentagonal prism is h=7 units.
The height is h=7 units.
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