To find side $ a $ use formula:

$$ V = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot l }{ 4 } $$

After substituting $V = 256\, \text{cm}$ and $l = 12.4\, \text{cm}$ we have:

$$ 256\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 12.4\, \text{cm} \right)^{4} }{ 4 } $$$$ 256\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 12.4\, \text{cm} \right)^{4} $$$$ 1024\, \text{cm} = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 12.4\, \text{cm} \right)^{4} $$$$ 1024\, \text{cm} = 21.4774\, \text{cm} \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 1024\, \text{cm}}{ 21.4774\, \text{cm} } $$$$ a ^{ 2 } \approx 15.1763 $$$$ a \approx \sqrt{ 15.1763 } $$$$ a \approx 3.8957 $$

Triangular Prism Calculator