STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $r = 72.8\, \text{cm}$ we have:

$$ 72.8\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 72.8\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 145.6\, \text{cm} $$ $$ a = \dfrac{ 145.6\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a \approx 84.0622\, \text{cm} $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 6 \cdot a $$

After substituting $a = 84.0622\, \text{cm}$ we have:

$$ P = 6 \cdot 84.0622\, \text{cm} $$ $$ P \approx 504.3732\, \text{cm} $$

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