Find the incircle radius $ r $ of a hexagon if short diagonal $s = \frac{ 7 }{ 2 }$.
Answer
$r = \frac{ 7 }{ 4 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ s = \sqrt{ 3 } \cdot a $$After substituting $ s = \frac{ 7 }{ 2 } $ we have:
$$ \frac{ 7 }{ 2 } = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ \frac{ 7 }{ 2 } }{ \sqrt{ 3 } } $$ $$ a = \frac{ 7 \sqrt{ 3}}{ 6 } $$STEP 2: find incircle radius $ r $
To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = \frac{ 7 \sqrt{ 3}}{ 6 } $ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot \frac{ 7 \sqrt{ 3}}{ 6 } }{ 2 } $$$$ r = \dfrac{ \frac{ 7 }{ 2 } }{ 2 } $$ $$ r = \frac{ 7 }{ 4 } $$This page was created using
Hexagon Calculator