Find the perimeter $ P $ of a hexagon if incircle radius $r = \frac{ 364 }{ 5 }$.

$P = \frac{ 1456 \sqrt{ 3}}{ 5 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ r = \frac{ 364 }{ 5 } $ we have:

$$ \frac{ 364 }{ 5 } = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = \frac{ 364 }{ 5 } \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = \frac{ 728 }{ 5 } $$ $$ a = \dfrac{ \frac{ 728 }{ 5 } }{ \sqrt{ 3 } } $$ $$ a = \frac{ 728 \sqrt{ 3}}{ 15 } $$

STEP 2: find perimeter $ P $

To find perimeter $ P $ use formula:

$$ P = 6 \cdot a $$

After substituting $ a = \frac{ 728 \sqrt{ 3}}{ 15 } $ we have:

$$ P = 6 \cdot \frac{ 728 \sqrt{ 3}}{ 15 } $$ $$ P = \frac{ 1456 \sqrt{ 3}}{ 5 } $$

Hexagon Calculator