Find the area $ A $ of a hexagon if incircle radius $r = \frac{ 39 }{ 2 }$.

$A = \frac{ 1521 \sqrt{ 3}}{ 2 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ r = \frac{ 39 }{ 2 } $ we have:

$$ \frac{ 39 }{ 2 } = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = \frac{ 39 }{ 2 } \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 39 $$ $$ a = \dfrac{ 39 }{ \sqrt{ 3 } } $$ $$ a = 13 \sqrt{ 3 } $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ a = 13 \sqrt{ 3 } $ we have:

$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \left(13 \sqrt{ 3 }\right)^2 }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 507 }{ 2 }$$ $$ A = \dfrac{ 1521 \sqrt{ 3 } }{ 2 }$$ $$ A = \frac{ 1521 \sqrt{ 3}}{ 2 } $$

Hexagon Calculator