Given:
The base area of the pentagonal prism
[tex]=39.1\text{ units}^2.[/tex]
The volume of the pentagonal prism
[tex]=273.7\text{ units}^3.[/tex]
Required:
We have to find the height.
Explanation:
The formula for the volume of the pentagonal prism is
[tex]\frac{5}{2}\times\text{ area of base}\times\text{ height.}[/tex]
Therefore, we can equate the given volume with the above formula.
Then proceed as follows:
[tex]\begin{gathered} \frac{5}{2}\times\text{ area of base}\times\text{ height}=273.7 \\ \Rightarrow\frac{5}{2}\times39.1\times\text{ height}=273.7 \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow\text{ height}=\frac{273.7\times2}{5\times39.1} \\ \\ \Rightarrow\text{ height}=\frac{547.4}{195.5} \end{gathered}[/tex][tex]\Rightarrow\text{ height}=2.8\text{ cm.}[/tex]
Final answer:
Hence the final answer is
[tex]2.8\text{ cm.}[/tex]
