Find the long diagonal $ d $ of a hexagon if short diagonal $s = \frac{ 1 }{ 4 }$.
Answer
$d = \frac{\sqrt{ 3 }}{ 6 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ s = \sqrt{ 3 } \cdot a $$After substituting $ s = \frac{ 1 }{ 4 } $ we have:
$$ \frac{ 1 }{ 4 } = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ \frac{ 1 }{ 4 } }{ \sqrt{ 3 } } $$ $$ a = \frac{\sqrt{ 3 }}{ 12 } $$STEP 2: find diagonal $ d $
To find diagonal $ d $ use formula:
$$ d = 2 \cdot a $$After substituting $ a = \frac{\sqrt{ 3 }}{ 12 } $ we have:
$$ d = 2 \cdot \frac{\sqrt{ 3 }}{ 12 } $$ $$ d = \frac{\sqrt{ 3 }}{ 6 } $$This page was created using
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