To find length $ l $ use formula:

$$ A = \frac{ a^2 \sqrt{3}}{2} + 3 a l $$

After substituting $A = 229.2\, \text{cm}$ and $a = 6\, \text{cm}$ we have:

$$ 229.2\, \text{cm} = \frac{ 6\, \text{cm}^2 \sqrt{3}}{2} + 3 \cdot 6\, \text{cm} \cdot l $$$$ 229.2\, \text{cm} = \frac{ 36\, \text{cm}^2 \sqrt{3}}{2} + 18\, \text{cm} \cdot l $$$$ 2 \cdot 229.2\, \text{cm} = 36 \sqrt{ 3 }\, \text{cm}^2 + 2 \cdot 18\, \text{cm} \cdot l $$$$ 458.4\, \text{cm} = 36 \sqrt{ 3 }\, \text{cm}^2 + 36\, \text{cm} \cdot l $$$$ 36\, \text{cm} \cdot l = 458.4\, \text{cm} - 36 \sqrt{ 3 }\, \text{cm}^2 $$$$ l = \frac{ 458.4\, \text{cm} - 36 \sqrt{ 3 }\, \text{cm}^2 }{ 36\, \text{cm} }$$$$ l = \frac{ 396.0462\, \text{cm} }{ 36\, \text{cm} }$$$$ l = 11.0013 $$

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