STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $\alpha = 52^o$ and $d_2 = 12.8\, \text{cm}$ we have:

$$ \sin \left( \frac{ 52^o }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$ $$ \sin( 26^o ) = \dfrac{ 12.8\, \text{cm} }{ d_1 } $$ $$ 0.4384 = \dfrac{ 12.8\, \text{cm} }{ d_1 } $$ $$ d_1 = \dfrac{ 12.8\, \text{cm} }{ 0.4384 } $$ $$ d_1 = 29.199\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $d_1 = 29.199\, \text{cm}$ and $d_2 = 12.8\, \text{cm}$ we have:

$$ A = \dfrac{ 29.199\, \text{cm} \cdot 12.8\, \text{cm} }{ 2 }$$$$ A = \dfrac{ 373.7472\, \text{cm}^2 }{ 2 } $$$$ A = 186.8736\, \text{cm}^2 $$

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