Question
Find the long diagonal $ d $ of a hexagon if short diagonal $s = \frac{ 9 }{ 32 }\, \text{cm}$.
Answer
$\dfrac{ 3 \sqrt{ 3}}{ 16 }\, \text{cm}$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ s = \sqrt{ 3 } \cdot a $$After substituting $s = \dfrac{ 9 }{ 32 }\, \text{cm}$ we have:
$$ \frac{ 9 }{ 32 }\, \text{cm} = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ \frac{ 9 }{ 32 }\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = \frac{ 3 \sqrt{ 3}}{ 32 }\, \text{cm} $$STEP 2: find diagonal $ d $
To find diagonal $ d $ use formula:
$$ d = 2 \cdot a $$After substituting $a = \dfrac{ 3 \sqrt{ 3}}{ 32 }\, \text{cm}$ we have:
$$ d = 2 \cdot \frac{ 3 \sqrt{ 3}}{ 32 }\, \text{cm} $$ $$ d = \frac{ 3 \sqrt{ 3}}{ 16 }\, \text{cm} $$This page was created using
Hexagon Calculator