Find the incircle radius $ r $ of a hexagon if area $A = 100$.

$r = 5.3728$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$

After substituting $ A = 100 $ we have:

$$ 100 = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$ $$ 100 \cdot 2 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ 200 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 200 }{ 3 \sqrt{ 3 } } $$ $$ a^2 = \frac{ 200 \sqrt{ 3}}{ 9 } $$ $$ a = \sqrt{ \frac{ 200 \sqrt{ 3}}{ 9 } } $$$$ a \approx 6.204 $$

STEP 2: find incircle radius $ r $

To find incircle radius $ r $ use formula:

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

After substituting $ a = 6.204 $ we have:

$$ r = \dfrac{ \sqrt{ 3 } \cdot 6.204 }{ 2 } $$$$ r = \dfrac{ 10.7457 }{ 2 } $$ $$ r \approx 5.3728 $$

Hexagon Calculator