STEP 1: find height $ h $

To find height $ h $ use formula:

$$ A = a \cdot h $$

After substituting $A = 214\, \text{cm}$ and $a = 16\, \text{cm}$ we have:

$$ 214\, \text{cm} = 16\, \text{cm} \cdot h $$$$ h = \dfrac{ 214\, \text{cm} }{ 16\, \text{cm} } $$$$ h = \frac{ 107 }{ 8 } $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$

After substituting $h = \dfrac{ 107 }{ 8 }\, \text{cm}^0$ and $a = 16\, \text{cm}$ we have:

$$ \sin \left( \alpha \right) = \dfrac{ \frac{ 107 }{ 8 } }{ 16\, \text{cm} } $$ $$ \sin \left( \alpha \right) = \frac{ 107 }{ 128 }\, \text{cm}^-1 $$ $$ \alpha = \arcsin\left( \frac{ 107 }{ 128 }\, \text{cm}^-1 \right) $$ $$ \alpha = 56.7136^o $$

STEP 3: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $\alpha = 56.7136^o$ and $h = \dfrac{ 107 }{ 8 }\, \text{cm}^0$ we have:

$$ \sin \left( \frac{ 56.7136^o }{ 2 } \right) = \dfrac{ h }{ d_1 } $$ $$ \sin( 28.3568 ) = \dfrac{ \frac{ 107 }{ 8 } }{ d_1 } $$ $$ 0.475 = \dfrac{ \frac{ 107 }{ 8 } }{ d_1 } $$ $$ d_1 = \dfrac{ \frac{ 107 }{ 8 } }{ 0.475 } $$ $$ d_1 = 28.1602 $$

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