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William Smith · Answer 1 · 2023-10-19T03:07:52+0000

$h=11.5\operatorname{cm}$

1) The Volume of that prism can be found by using this formula:

$V=A_b\cdot h$

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:

$A=s^2\Rightarrow A=6^2\Rightarrow A=36$

So now, let's plug into that both volume and Area to get the height of that prism.

$\begin{gathered} 414=36h \\ (414)/(36)=(36h)/(36) \\ (23)/(2)=h \\ h=11.5\operatorname{cm} \end{gathered}$

3) Thus, the height of that prism is 11.5 cm.

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