Find the area $ A $ of a hexagon if circumcircle radius $R = \frac{ 3 }{ 2 }$.
Answer
$A = \frac{ 27 \sqrt{ 3}}{ 8 }$
Explanation
STEP 1:
The side of the hexagon is equal the radius of the circumcircle. $$ a = \frac{ 3 }{ 2 } $$
STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 } $$After substituting $ a = \frac{ 3 }{ 2 } $ we have:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \left(\frac{ 3 }{ 2 }\right)^2 }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \frac{ 9 }{ 4 } }{ 2 }$$ $$ A = \dfrac{ \frac{ 27 \sqrt{ 3}}{ 4 } }{ 2 }$$ $$ A = \frac{ 27 \sqrt{ 3}}{ 8 } $$This page was created using
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