Find the area $ A $ of a hexagon if circumcircle radius $R = 4 \sqrt{ 6 }$.
Answer
$A = 144 \sqrt{ 3 }$
Explanation
STEP 1:
The side of the hexagon is equal the radius of the circumcircle. $$ a = 4 \sqrt{ 6 } $$
STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 } $$After substituting $ a = 4 \sqrt{ 6 } $ we have:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \left(4 \sqrt{ 6 }\right)^2 }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 96 }{ 2 }$$ $$ A = \dfrac{ 288 \sqrt{ 3 } }{ 2 }$$ $$ A = 144 \sqrt{ 3 } $$This page was created using
Hexagon Calculator