STEP 1: Transform all variables to millimeters.

$$ l = 6\, \text{cm} = 6 \cdot \left( 10 \text{ mm}\right) = 60\, \text{mm} $$$$ V = 264\, \text{mm}^3 $$

STEP 2: find side $ a $

To find side $ a $ use formula:

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

After substituting $V = 264\, \text{mm}^3$ and $l = 60\, \text{mm}$ we have:

$$ 264\, \text{mm}^3 = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 60\, \text{mm} \right)^{4} }{ 4 } $$$$ 264\, \text{mm}^3 \cdot 4 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 60\, \text{mm} \right)^{4} $$$$ 1056\, \text{mm}^3 = \sqrt{ 3 } \cdot a ^{ 2 } \cdot \left( 60\, \text{mm} \right)^{4} $$$$ 1056\, \text{mm}^3 = 60 \sqrt{ 3 }\, \text{mm} \cdot a ^{ 2 } $$$$ a ^{ 2 } = \dfrac{ 1056\, \text{mm}^3}{ 60 \sqrt{ 3 }\, \text{mm} } $$$$ a ^{ 2 } \approx 3.2345\, \text{mm}^2 $$$$ a \approx \sqrt{ 3.2345\, \text{mm}^2 } $$$$ a \approx 1.7985\, \text{mm} $$

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