Find the side $ a $ of a triangular prism if length $l = 21$ and volume $V = 1102.5$.

$a = 7.786$

To find side $ a $ use formula:

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

After substituting $ V = 1102.5 $ and $ l = 21 $ we have:

$$ 1102.5 = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot 21 }{ 2 } $$$$ 1102.5 \cdot 2 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 21 $$$$ 2205 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot 21 $$$$ 2205 = 21 \sqrt{ 3 } \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 2205}{ 21 \sqrt{ 3 } } $$$$ a ^{ 2 } = 60.6218 $$$$ a = \sqrt{ 60.6218 } $$$$ a = 7.786 $$

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