Find the long diagonal $ d $ of a hexagon if incircle radius $r = 9$.
Answer
$d = 12 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ r = 9 $ we have:
$$ 9 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 9 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 18 $$ $$ a = \dfrac{ 18 }{ \sqrt{ 3 } } $$ $$ a = 6 \sqrt{ 3 } $$STEP 2: find diagonal $ d $
To find diagonal $ d $ use formula:
$$ d = 2 \cdot a $$After substituting $ a = 6 \sqrt{ 3 } $ we have:
$$ d = 2 \cdot 6 \sqrt{ 3 } $$ $$ d = 12 \sqrt{ 3 } $$This page was created using
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