STEP 1: find side $ a $

To find side $ a $ use formula:

$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$

After substituting $r = 10.4\, \text{cm}$ we have:

$$ 10.4\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 10.4\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 20.8\, \text{cm} $$ $$ a = \dfrac{ 20.8\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a \approx 12.0089\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $a = 12.0089\, \text{cm}$ we have:

$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \left( 12.0089\, \text{cm} \right)^{2} }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 144.2133\, \text{cm}^2 }{ 2 }$$ $$ A = \dfrac{ 749.3545\, \text{cm}^2 }{ 2 }$$ $$ A = 374.6772\, \text{cm}^2 $$

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