STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $A = 480\, \text{cm}$ and $d_2 = 48\, \text{cm}$ we have:

$$ 480\, \text{cm} = \dfrac{ d_1 \cdot \left( 48\, \text{cm} \right)^{4} }{ 2 } $$$$ 480\, \text{cm} \cdot 2 = d_1 \cdot \left( 48\, \text{cm} \right)^{4} $$$$ 960\, \text{cm} = 48\, \text{cm} \cdot d_1 $$$$ d_1 = \dfrac{ 960\, \text{cm}}{ 48\, \text{cm} } $$$$ d_1 \approx 6.3662 $$

STEP 2: find side $ a $

To find side $ a $ use formula:

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

After substituting $d_1 = 6.3662\, \text{cm}^0$ and $d_2 = 48\, \text{cm}$ we have:

$$ 6.3662 + \left( 48\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 40.5283 + 2304\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 2344.5283 $$ $$ a^2 = \frac{ 2344.5283 }{ 4 } $$ $$ a^2 = 586.1321 $$ $$ a = \sqrt{ 586.1321 } $$$$ a = 24.2102 $$

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