Question
Find the area $ A $ of a hexagon if circumcircle radius $R = 13\, \text{cm}$.
Answer
$\dfrac{ 507 \sqrt{ 3}}{ 2 }\, \text{cm}^2$
Explanation
STEP 1:
The side of the hexagon is equal the radius of the circumcircle. $$ a = 13 $$
STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 } $$After substituting $a = 13\, \text{cm}$ we have:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot \left( 13\, \text{cm} \right)^{2} }{ 2 } $$ $$ A = \dfrac{ 3 \sqrt{ 3 } \cdot 169\, \text{cm}^2 }{ 2 }$$ $$ A = \dfrac{ 507 \sqrt{ 3 }\, \text{cm}^2 }{ 2 }$$ $$ A = \frac{ 507 \sqrt{ 3}}{ 2 }\, \text{cm}^2 $$This page was created using
Hexagon Calculator