Find the side $ a $ of a hexagon if area $A = 72 \sqrt{ 3 }$.
Answer
$a = 4 \sqrt{ 3 }$
Explanation
To find side $ a $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$After substituting $ A = 72 \sqrt{ 3 } $ we have:
$$ 72 \sqrt{ 3 } = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$ $$ 72 \sqrt{ 3 } \cdot 2 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ 144 \sqrt{ 3 } = 3 \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 144 \sqrt{ 3 } }{ 3 \sqrt{ 3 } } $$ $$ a^2 = 48 $$ $$ a = \sqrt{ 48 } $$ $$ a = 4 \sqrt{ 3 } $$This page was created using
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