Find the incircle radius $ r $ of a hexagon if short diagonal $s = 40$.
Answer
$r = 20$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ s = \sqrt{ 3 } \cdot a $$After substituting $ s = 40 $ we have:
$$ 40 = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ 40 }{ \sqrt{ 3 } } $$ $$ a = \frac{ 40 \sqrt{ 3}}{ 3 } $$STEP 2: find incircle radius $ r $
To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = \frac{ 40 \sqrt{ 3}}{ 3 } $ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot \frac{ 40 \sqrt{ 3}}{ 3 } }{ 2 } $$$$ r = \dfrac{ 40 }{ 2 } $$ $$ r = 20 $$This page was created using
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