STEP 1: find side $ a $
To find side $ a $ use formula:
$$ A = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$After substituting $ A = 12 $ we have:
$$ 12 = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 12 \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 48 = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 48 }{ \sqrt{ 3 } } $$ $$ a^2 = 16 \sqrt{ 3 } $$ $$ a = \sqrt{ 16 \sqrt{ 3 } } $$$$ a \approx 5.2643 $$STEP 2: find height $ h $
To find height $ h $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = 5.2643 $ we have:
$$ h = \dfrac{ \sqrt{ 3 } \cdot 5.2643 }{ 2 } $$$$ h = \dfrac{ 9.118 }{ 2 } $$ $$ h \approx 4.559 $$