STEP 1: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

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

After substituting $A = 143\, \text{cm}$ and $d_1 = 26\, \text{cm}$ we have:

$$ 143\, \text{cm} = \dfrac{ 26\, \text{cm} \cdot d_2 }{ 2 } $$$$ 143\, \text{cm} \cdot 2 = 26\, \text{cm} \cdot d_2 $$$$ 286\, \text{cm} = 26\, \text{cm} \cdot d_2 $$$$ d_2 = \dfrac{ 286\, \text{cm} }{ 26\, \text{cm} } $$$$ d_2 = 11 $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $d_2 = 11\, \text{cm}^0$ and $d_1 = 26\, \text{cm}$ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 11 }{ 26\, \text{cm} } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 11 }{ 26 }\, \text{cm}^-1 $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 11 }{ 26 }\, \text{cm}^-1 \right) $$ $$ \frac{ \alpha }{ 2 } = 25.029^o $$$$ \alpha = 25.029^o \cdot 2 $$$$ \alpha = 50.058^o $$

STEP 3: find height $ h $

To find height $ h $ use formula:

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

After substituting $\alpha = 50.058^o$ and $d_1 = 26\, \text{cm}$ we have:

$$ \sin \left( \frac{ 50.058^o }{ 2 } \right) = \dfrac{ h }{ d_1 } $$ $$ \sin( 25.029 ) = \dfrac{ h }{ 26 } $$ $$ 0.4231 = \dfrac{ h }{ 26 } $$$$ h = 0.4231 \cdot 26 $$$$ h = 11 $$

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