[tex]h=11.5\operatorname{cm}[/tex]
1) The Volume of that prism can be found by using this formula:
[tex]V=A_b\cdot h[/tex]
Note that the volume has been given to us already: 414 cm³, so to find out the height of that volume, we just need to calculate the area of the base.
2) Note that the base is a square, then we can write out for the base:
[tex]A=s^2\Rightarrow A=6^2\Rightarrow A=36[/tex]
So now, let's plug into that both volume and Area to get the height of that prism.
[tex]\begin{gathered} 414=36h \\ \frac{414}{36}=\frac{36h}{36} \\ \frac{23}{2}=h \\ h=11.5\operatorname{cm} \end{gathered}[/tex]
3) Thus, the height of that prism is 11.5 cm.
