STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $r = 6\, \text{cm}$ we have:

$$ 6\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 6\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 12\, \text{cm} $$ $$ a = \dfrac{ 12\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = 4 \sqrt{ 3 }\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

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

$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \left( 4 \sqrt{ 3 }\, \text{cm} \right)^{2} }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 48\, \text{cm}^2 }{ 2 }$$ $$ A = \dfrac{ 144 \sqrt{ 3 }\, \text{cm}^2 }{ 2 }$$ $$ A = 72 \sqrt{ 3 }\, \text{cm}^2 $$

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