To find side $ a $ use formula:

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

After substituting $A = \dfrac{ 169 \sqrt{ 3}}{ 4 }\, \text{cm}$ we have:

$$ \frac{ 169 \sqrt{ 3}}{ 4 }\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ \frac{ 169 \sqrt{ 3}}{ 4 }\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 169 \sqrt{ 3 }\, \text{cm} = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 169 \sqrt{ 3 }\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a^2 = 169\, \text{cm} $$ $$ a = \sqrt{ 169\, \text{cm} } $$ $$ a = 13 $$

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