Find the side $ a $ of a hexagon if area $A = 100$.
Answer
$a = 6.204$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$After substituting $ A = 100 $ we have:
$$ 100 = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$ $$ 100 \cdot 2 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ 200 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 200 }{ 3 \sqrt{ 3 } } $$ $$ a^2 = \frac{ 200 \sqrt{ 3}}{ 9 } $$ $$ a = \sqrt{ \frac{ 200 \sqrt{ 3}}{ 9 } } $$$$ a \approx 6.204 $$This page was created using
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