Find the long diagonal $ d $ of a hexagon if incircle radius $r = \frac{ 45 }{ 2 }$.
Answer
$d = 30 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ r = \frac{ 45 }{ 2 } $ we have:
$$ \frac{ 45 }{ 2 } = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = \frac{ 45 }{ 2 } \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 45 $$ $$ a = \dfrac{ 45 }{ \sqrt{ 3 } } $$ $$ a = 15 \sqrt{ 3 } $$STEP 2: find diagonal $ d $
To find diagonal $ d $ use formula:
$$ d = 2 \cdot a $$After substituting $ a = 15 \sqrt{ 3 } $ we have:
$$ d = 2 \cdot 15 \sqrt{ 3 } $$ $$ d = 30 \sqrt{ 3 } $$This page was created using
Hexagon Calculator