STEP 1: find diagonal $ d2 $
To find diagonal $ d2 $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ A = 36 $ and $ d_1 = 8 $ we have:
$$ 36 = \dfrac{ 8 \cdot d_2 }{ 2 } $$$$ 36 \cdot 2 = 8 \cdot d_2 $$$$ 72 = 8 \cdot d_2 $$$$ d_2 = \dfrac{ 72 }{ 8 } $$$$ d_2 = 9 $$STEP 2: find side $ a $
To find side $ a $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 8 $ and $ d_2 = 9 $ we have:
$$ 8^2 + 9^2 = 4 \cdot a^2 $$ $$ 64 + 81 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 145 $$ $$ a^2 = \frac{ 145 }{ 4 } $$ $$ a^2 = \frac{ 145 }{ 4 } $$ $$ a = \sqrt{ \frac{ 145 }{ 4 } } $$$$ a = \frac{\sqrt{ 145 }}{ 2 } $$