STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $\alpha = 134^o$ and $d_2 = 11.2\, \text{cm}$ we have:

$$ \sin \left( \frac{ 134^o }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$ $$ \sin( 67^o ) = \dfrac{ 11.2\, \text{cm} }{ d_1 } $$ $$ 0.9205 = \dfrac{ 11.2\, \text{cm} }{ d_1 } $$ $$ d_1 = \dfrac{ 11.2\, \text{cm} }{ 0.9205 } $$ $$ d_1 = 12.1672\, \text{cm} $$

STEP 2: find side $ a $

To find side $ a $ use formula:

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

After substituting $d_1 = 12.1672\, \text{cm}$ and $d_2 = 11.2\, \text{cm}$ we have:

$$ \left( 12.1672\, \text{cm} \right)^{2} + \left( 11.2\, \text{cm} \right)^{2} = 4 \cdot a^2 $$ $$ 148.0416\, \text{cm}^2 + 125.44\, \text{cm}^2 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 273.4816\, \text{cm}^2 $$ $$ a^2 = \frac{ 273.4816\, \text{cm}^2 }{ 4 } $$ $$ a^2 = 68.3704\, \text{cm}^2 $$ $$ a = \sqrt{ 68.3704\, \text{cm}^2 } $$$$ a = 8.2686\, \text{cm} $$

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