STEP 1: find side $ a $

To find side $ a $ use formula:

$$ R = \dfrac{ \sqrt{ 3 } \cdot a }{ 3 } $$

After substituting $R = 5\, \text{cm}$ we have:

$$ 5\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 3 } $$ $$ \sqrt{ 3 } \cdot a = 5\, \text{cm} \cdot 3 $$ $$ \sqrt{ 3 } \cdot a = 15\, \text{cm} $$ $$ a = \dfrac{ 15\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = 5 \sqrt{ 3 }\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $a = 5 \sqrt{ 3 }\, \text{cm}$ we have:

$$ A = \dfrac{ \sqrt{ 3 } \cdot \left( 5 \sqrt{ 3 }\, \text{cm} \right)^{2} }{ 4 } $$ $$ A = \dfrac{ \sqrt{ 3 } \cdot 75\, \text{cm}^2 }{ 4 }$$ $$ A = \dfrac{ 75 \sqrt{ 3 }\, \text{cm}^2 }{ 4 }$$ $$ A = \frac{ 75 \sqrt{ 3}}{ 4 }\, \text{cm}^2 $$

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