Find the incircle radius $ r $ of a hexagon if long diagonal $d = \frac{ 5 }{ 2 }$.
Answer
$r = \frac{ 5 \sqrt{ 3}}{ 8 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = 2 \cdot a $$After substituting $ d = \frac{ 5 }{ 2 } $ we have:
$$ \frac{ 5 }{ 2 } = 2 \cdot a $$ $$ a = \dfrac{ \frac{ 5 }{ 2 } }{ 2 } $$ $$ a = \frac{ 5 }{ 4 } $$STEP 2: find incircle radius $ r $
To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = \frac{ 5 }{ 4 } $ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot \frac{ 5 }{ 4 } }{ 2 } $$$$ r = \dfrac{ \frac{ 5 \sqrt{ 3}}{ 4 } }{ 2 } $$ $$ r = \frac{ 5 \sqrt{ 3}}{ 8 } $$This page was created using
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