STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $r = 10\, \text{cm}$ we have:

$$ 10\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$ $$ \sqrt{ 3 } \cdot a = 10\, \text{cm} \cdot 6 $$ $$ \sqrt{ 3 } \cdot a = 60\, \text{cm} $$ $$ a = \dfrac{ 60\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = 20 \sqrt{ 3 }\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 } $$

After substituting $a = 20 \sqrt{ 3 }\, \text{cm}$ we have:

$$ A = \dfrac{ \sqrt{ 3 } \cdot \left( 20 \sqrt{ 3 }\, \text{cm} \right)^{2} }{ 4 } $$ $$ A = \dfrac{ \sqrt{ 3 } \cdot 1200\, \text{cm}^2 }{ 4 }$$ $$ A = \dfrac{ 1200 \sqrt{ 3 }\, \text{cm}^2 }{ 4 }$$ $$ A = 300 \sqrt{ 3 }\, \text{cm}^2 $$

Equilateral Triangle Calculator