Find the side $ a $ of a triangular prism if length $l = 12.4$ and volume $V = 256$.

$a = 4.8825$

To find side $ a $ use formula:

$$ V = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot l }{ 2 } $$

After substituting $ V = 256 $ and $ l = 12.4 $ we have:

$$ 256 = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot 12.4 }{ 2 } $$$$ 256 \cdot 2 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 12.4 $$$$ 512 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 12.4 $$$$ 512 = 21.4774 \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 512}{ 21.4774 } $$$$ a ^{ 2 } = 23.839 $$$$ a = \sqrt{ 23.839 } $$$$ a = 4.8825 $$

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