To find side $ a $ use formula:

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

After substituting $A = 35.6\, \text{cm}$ we have:

$$ 35.6\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 35.6\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 142.4\, \text{cm} = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 142.4\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a^2 = 82.2147\, \text{cm} $$ $$ a = \sqrt{ 82.2147\, \text{cm} } $$$$ a \approx 9.0672 $$

Equilateral Triangle Calculator