Find the circumcircle radius $ R $ of a hexagon if area $A = 12$.
Answer
$R = 2.1491$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$After substituting $ A = 12 $ we have:
$$ 12 = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$ $$ 12 \cdot 2 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ 24 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 24 }{ 3 \sqrt{ 3 } } $$ $$ a^2 = \frac{ 8 \sqrt{ 3}}{ 3 } $$ $$ a = \sqrt{ \frac{ 8 \sqrt{ 3}}{ 3 } } $$$$ a \approx 2.1491 $$STEP 2:
The radius of the circumcircle is equal the side of the hexagon. $$ R = 2.1491 $$
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