STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $A = 20\, \text{cm}$ and $d_2 = 5\, \text{cm}$ we have:

$$ 20\, \text{cm} = \dfrac{ d_1 \cdot \left( 5\, \text{cm} \right)^{4} }{ 2 } $$$$ 20\, \text{cm} \cdot 2 = d_1 \cdot \left( 5\, \text{cm} \right)^{4} $$$$ 40\, \text{cm} = 5\, \text{cm} \cdot d_1 $$$$ d_1 = \dfrac{ 40\, \text{cm}}{ 5\, \text{cm} } $$$$ d_1 \approx 2.5465 $$

STEP 2: find side $ a $

To find side $ a $ use formula:

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

After substituting $d_1 = 2.5465\, \text{cm}^0$ and $d_2 = 5\, \text{cm}$ we have:

$$ 2.5465 + \left( 5\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 6.4845 + 25\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 31.4845 $$ $$ a^2 = \frac{ 31.4845 }{ 4 } $$ $$ a^2 = 7.8711 $$ $$ a = \sqrt{ 7.8711 } $$$$ a = 2.8056 $$

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