Find the short diagonal $ s $ of a hexagon if long diagonal $d = \frac{ 72 }{ 5 }$.
Answer
$s = \frac{ 36 \sqrt{ 3}}{ 5 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = 2 \cdot a $$After substituting $ d = \frac{ 72 }{ 5 } $ we have:
$$ \frac{ 72 }{ 5 } = 2 \cdot a $$ $$ a = \dfrac{ \frac{ 72 }{ 5 } }{ 2 } $$ $$ a = \frac{ 36 }{ 5 } $$STEP 2: find diagonal $ s $
To find diagonal $ s $ use formula:
$$ s = \sqrt{ 3 } \cdot a $$After substituting $ a = \frac{ 36 }{ 5 } $ we have:
$$ s = \sqrt{ 3 } \cdot \frac{ 36 }{ 5 } $$ $$ s = \frac{ 36 \sqrt{ 3}}{ 5 } $$This page was created using
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