STEP 1: find side $ a $
To find side $ a $ use formula:
$$ A = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$After substituting $ A = 142 $ we have:
$$ 142 = \dfrac{ 3 \sqrt{ 3 } \cdot a^2 }{ 2 }$$ $$ 142 \cdot 2 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ 284 = 3 \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 284 }{ 3 \sqrt{ 3 } } $$ $$ a^2 = \frac{ 284 \sqrt{ 3}}{ 9 } $$ $$ a = \sqrt{ \frac{ 284 \sqrt{ 3}}{ 9 } } $$$$ a \approx 7.393 $$STEP 2: find perimeter $ P $
To find perimeter $ P $ use formula:
$$ P = 6 \cdot a $$After substituting $ a = 7.393 $ we have:
$$ P = 6 \cdot 7.393 $$ $$ P \approx 44.3577 $$