Find the area $ A $ of a hexagon if circumcircle radius $R = 3$.
Answer
$A = \frac{ 27 \sqrt{ 3}}{ 2 }$
Explanation
STEP 1:
The side of the hexagon is equal the radius of the circumcircle. $$ a = 3 $$
STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 } $$After substituting $ a = 3 $ we have:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 3^2 }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 9 }{ 2 }$$ $$ A = \dfrac{ 27 \sqrt{ 3 } }{ 2 }$$ $$ A = \frac{ 27 \sqrt{ 3}}{ 2 } $$This page was created using
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