STEP 1: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$

After substituting $A = 42\, \text{cm}$ and $d_1 = 8\, \text{cm}$ we have:

$$ 42\, \text{cm} = \dfrac{ 8\, \text{cm} \cdot d_2 }{ 2 } $$$$ 42\, \text{cm} \cdot 2 = 8\, \text{cm} \cdot d_2 $$$$ 84\, \text{cm} = 8\, \text{cm} \cdot d_2 $$$$ d_2 = \dfrac{ 84\, \text{cm} }{ 8\, \text{cm} } $$$$ d_2 = \frac{ 21 }{ 2 } $$

STEP 2: find side $ a $

To find side $ a $ use formula:

$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$

After substituting $d_1 = 8\, \text{cm}$ and $d_2 = \dfrac{ 21 }{ 2 }\, \text{cm}^0$ we have:

$$ \left( 8\, \text{cm} \right)^{2} + \frac{ 21 }{ 2 } = 4 \cdot a^2 $$ $$ 64\, \text{cm}^2 + \frac{ 441 }{ 4 } = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = \frac{ 697 }{ 4 }\, \text{cm}^2 $$ $$ a^2 = \frac{ \frac{ 697 }{ 4 }\, \text{cm}^2 }{ 4 } $$ $$ a^2 = \frac{ 697 }{ 16 }\, \text{cm}^2 $$ $$ a = \sqrt{ \frac{ 697 }{ 16 }\, \text{cm}^2 } $$$$ a = \frac{\sqrt{ 697 }}{ 4 }\, \text{cm} $$

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