STEP 1: find side $ a $
To find side $ a $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$After substituting $ A = 72 \sqrt{ 3 } $ we have:
$$ 72 \sqrt{ 3 } = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$ $$ 72 \sqrt{ 3 } \cdot 2 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ 144 \sqrt{ 3 } = 3 \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 144 \sqrt{ 3 } }{ 3 \sqrt{ 3 } } $$ $$ a^2 = 48 $$ $$ a = \sqrt{ 48 } $$ $$ a = 4 \sqrt{ 3 } $$STEP 2:
The radius of the circumcircle is equal the side of the hexagon. $$ R = 4 \sqrt{ 3 } $$