To find side $ a $ use formula:

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

After substituting $A = 1\, \text{cm}$ we have:

$$ 1\, \text{cm} = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$ $$ 1\, \text{cm} \cdot 2 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ 2\, \text{cm} = 3 \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 2\, \text{cm} }{ 3 \sqrt{ 3 } } $$ $$ a^2 = \frac{ 2 \sqrt{ 3}}{ 9 }\, \text{cm} $$ $$ a = \sqrt{ \frac{ 2 \sqrt{ 3}}{ 9 }\, \text{cm} } $$$$ a \approx 0.6204 $$

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