Find the side $ a $ of a triangular prism if length $l = 16$ and volume $V = 224$.

$a = 4.0207$

To find side $ a $ use formula:

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

After substituting $ V = 224 $ and $ l = 16 $ we have:

$$ 224 = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot 16 }{ 2 } $$$$ 224 \cdot 2 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 16 $$$$ 448 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 16 $$$$ 448 = 16 \sqrt{ 3 } \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 448}{ 16 \sqrt{ 3 } } $$$$ a ^{ 2 } = \frac{ 28 \sqrt{ 3}}{ 3 } $$$$ a = \sqrt{ \frac{ 28 \sqrt{ 3}}{ 3 } } $$$$ a = 4.0207 $$

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