STEP 1: find side $ a $

To find side $ a $ use formula:

$$ s = \sqrt{ 3 } \cdot a $$

After substituting $s = 40\, \text{cm}$ we have:

$$ 40\, \text{cm} = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ 40\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = \frac{ 40 \sqrt{ 3}}{ 3 }\, \text{cm} $$

STEP 2: find incircle radius $ r $

To find incircle radius $ r $ use formula:

$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$

After substituting $a = \dfrac{ 40 \sqrt{ 3}}{ 3 }\, \text{cm}$ we have:

$$ r = \dfrac{ \sqrt{ 3 } \cdot \frac{ 40 \sqrt{ 3}}{ 3 }\, \text{cm} }{ 2 } $$$$ r = \dfrac{ 40\, \text{cm} }{ 2 } $$ $$ r = 20\, \text{cm} $$

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