Find the side $ a $ of a hexagon if incircle radius $r = \frac{ 5 }{ 4 }$.
Answer
$a = \frac{ 5 \sqrt{ 3}}{ 6 }$
Explanation
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ r = \frac{ 5 }{ 4 } $ we have:
$$ \frac{ 5 }{ 4 } = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = \frac{ 5 }{ 4 } \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = \frac{ 5 }{ 2 } $$ $$ a = \dfrac{ \frac{ 5 }{ 2 } }{ \sqrt{ 3 } } $$ $$ a = \frac{ 5 \sqrt{ 3}}{ 6 } $$This page was created using
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