STEP 1: find side $ a $

To find side $ a $ use formula:

$$ R = \dfrac{ \sqrt{ 2 } \cdot a }{ 2 } $$

After substituting $R = 8 \sqrt{ 2 }\, \text{cm}$ we have:

$$ 8 \sqrt{ 2 }\, \text{cm} = \dfrac{ \sqrt{ 2 } \cdot a }{ 2 } $$ $$ \sqrt{ 2 } \cdot a = 8 \sqrt{ 2 }\, \text{cm} \cdot 2 $$ $$ \sqrt{ 2 } \cdot a = 16 \sqrt{ 2 }\, \text{cm} $$ $$ a = \dfrac{ 16 \sqrt{ 2 }\, \text{cm} }{ \sqrt{ 2 } } $$ $$ a = 16\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = a^2 $$

After substituting $a = 16\, \text{cm}$ we have:

$$ A = \left( 16\, \text{cm} \right)^{2} $$ $$ A = 256\, \text{cm}^2 $$

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