STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $A = 12\, \text{cm}$ we have:

$$ 12\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 12\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 48\, \text{cm} = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 48\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a^2 = 16 \sqrt{ 3 }\, \text{cm} $$ $$ a = \sqrt{ 16 \sqrt{ 3 }\, \text{cm} } $$$$ a \approx 5.2643 $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $a = 5.2643\, \text{cm}^0$ we have:

$$ h = \dfrac{ \sqrt{ 3 } \cdot 5.2643 }{ 2 } $$$$ h = \dfrac{ 9.118 }{ 2 } $$ $$ h \approx 4.559 $$

Equilateral Triangle Calculator