STEP 1: find side $ a $

To find side $ a $ use formula:

$$ P = 3 \cdot a $$

After substituting $P = 510\, \text{cm}$ we have:

$$ 510\, \text{cm} = 3 \cdot a $$ $$ a = \dfrac{ 510\, \text{cm} }{ 3 } $$ $$ a = 170\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $a = 170\, \text{cm}$ we have:

$$ A = \dfrac{ \sqrt{ 3 } \cdot \left( 170\, \text{cm} \right)^{2} }{ 4 } $$ $$ A = \dfrac{ \sqrt{ 3 } \cdot 28900\, \text{cm}^2 }{ 4 }$$ $$ A = \dfrac{ 28900 \sqrt{ 3 }\, \text{cm}^2 }{ 4 }$$ $$ A = 7225 \sqrt{ 3 }\, \text{cm}^2 $$

Equilateral Triangle Calculator