Question
Find the incircle radius $ r $ of a hexagon if circumcircle radius $R = 30\, \text{cm}$.
Answer
$15 \sqrt{ 3 }\, \text{cm}$
Explanation
STEP 1:
The side of the hexagon is equal the radius of the circumcircle. $$ a = 30 $$
STEP 2: find incircle radius $ r $
To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $a = 30\, \text{cm}$ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot 30\, \text{cm} }{ 2 } $$$$ r = \dfrac{ 30 \sqrt{ 3 }\, \text{cm} }{ 2 } $$ $$ r = 15 \sqrt{ 3 }\, \text{cm} $$This page was created using
Hexagon Calculator