STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $r = 2\, \text{cm}$ we have:

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

STEP 2: find diagonal $ d $

To find diagonal $ d $ use formula:

$$ d = 2 \cdot a $$

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

$$ d = 2 \cdot \frac{ 4 \sqrt{ 3}}{ 3 }\, \text{cm} $$ $$ d = \frac{ 8 \sqrt{ 3}}{ 3 }\, \text{cm} $$

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