STEP 1: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

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

After substituting $A = 500\, \text{cm}$ and $d_1 = 25\, \text{cm}$ we have:

$$ 500\, \text{cm} = \dfrac{ 25\, \text{cm} \cdot d_2 }{ 2 } $$$$ 500\, \text{cm} \cdot 2 = 25\, \text{cm} \cdot d_2 $$$$ 1000\, \text{cm} = 25\, \text{cm} \cdot d_2 $$$$ d_2 = \dfrac{ 1000\, \text{cm} }{ 25\, \text{cm} } $$$$ d_2 = 40 $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$

After substituting $d_2 = 40\, \text{cm}^0$ and $d_1 = 25\, \text{cm}$ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 40 }{ 25\, \text{cm} } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 8 }{ 5 }\, \text{cm}^-1 $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 8 }{ 5 }\, \text{cm}^-1 \right) $$

$ \arcsin(1.6) $ is not defined $ \Longrightarrow $ The problem has no solution.

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