Question
Find the incircle radius $ r $ of a hexagon if short diagonal $s = 3.5\, \text{cm}$.
Answer
$1.75\, \text{cm}$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ s = \sqrt{ 3 } \cdot a $$After substituting $s = 3.5\, \text{cm}$ we have:
$$ 3.5\, \text{cm} = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ 3.5\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a \approx 2.0207\, \text{cm} $$STEP 2: find incircle radius $ r $
To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $a = 2.0207\, \text{cm}$ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot 2.0207\, \text{cm} }{ 2 } $$$$ r = \dfrac{ 3.5\, \text{cm} }{ 2 } $$ $$ r = 1.75\, \text{cm} $$This page was created using
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