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What is the vertical height, h, of the triangular prism?

What is the vertical height, h, of the triangular prism?-example-1

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\begin{gathered} h^2=(3\sqrt[]{2})^2-3^2=9\cdot4-9=27^{} \\ h=\sqrt[]{27}=3\sqrt[]{3} \end{gathered}

What is the vertical height, h, of the triangular prism?-example-1
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