STEP 1: find side $ a $

To find side $ a $ use formula:

$$ R = \dfrac{ \sqrt{ 3 } \cdot a }{ 3 } $$

After substituting $R = 1\, \text{cm}$ we have:

$$ 1\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 3 } $$ $$ \sqrt{ 3 } \cdot a = 1\, \text{cm} \cdot 3 $$ $$ \sqrt{ 3 } \cdot a = 3\, \text{cm} $$ $$ a = \dfrac{ 3\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = \sqrt{ 3 }\, \text{cm} $$

STEP 2: find incircle radius $ r $

To find incircle radius $ r $ use formula:

$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$

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

$$ r = \dfrac{ \sqrt{ 3 } \cdot \sqrt{ 3 }\, \text{cm} }{ 6 } $$$$ r = \dfrac{ 3\, \text{cm} }{ 6 } $$ $$ r = \frac{ 1 }{ 2 }\, \text{cm} $$

Equilateral Triangle Calculator