Find the incircle radius $ r $ of a hexagon if long diagonal $d = 180$.
Answer
$r = 45 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = 2 \cdot a $$After substituting $ d = 180 $ we have:
$$ 180 = 2 \cdot a $$ $$ a = \dfrac{ 180 }{ 2 } $$ $$ a = 90 $$STEP 2: find incircle radius $ r $
To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = 90 $ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot 90 }{ 2 } $$$$ r = \dfrac{ 90 \sqrt{ 3 } }{ 2 } $$ $$ r = 45 \sqrt{ 3 } $$This page was created using
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