Find the side $ a $ of a hexagon if area $A = \frac{ 34641 }{ 5000 }$.

$a = 1.633$

To find side $ a $ use formula:

$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$

After substituting $ A = \frac{ 34641 }{ 5000 } $ we have:

$$ \frac{ 34641 }{ 5000 } = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$ $$ \frac{ 34641 }{ 5000 } \cdot 2 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ \frac{ 34641 }{ 2500 } = 3 \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ \frac{ 34641 }{ 2500 } }{ 3 \sqrt{ 3 } } $$ $$ a^2 = \frac{ 3849 \sqrt{ 3}}{ 2500 } $$ $$ a = \sqrt{ \frac{ 3849 \sqrt{ 3}}{ 2500 } } $$$$ a \approx 1.633 $$

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