STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $R = 2.12\, \text{cm}$ we have:

$$ 2.12\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 3 } $$ $$ \sqrt{ 3 } \cdot a = 2.12\, \text{cm} \cdot 3 $$ $$ \sqrt{ 3 } \cdot a = 6.36\, \text{cm} $$ $$ a = \dfrac{ 6.36\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a \approx 3.6719\, \text{cm} $$

STEP 2: find incircle radius $ r $

To find incircle radius $ r $ use formula:

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

After substituting $a = 3.6719\, \text{cm}$ we have:

$$ r = \dfrac{ \sqrt{ 3 } \cdot 3.6719\, \text{cm} }{ 6 } $$$$ r = \dfrac{ 6.36\, \text{cm} }{ 6 } $$ $$ r = 1.06\, \text{cm} $$

Equilateral Triangle Calculator