STEP 1: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

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

After substituting $A = 150\, \text{cm}$ and $d_1 = 30\, \text{cm}$ we have:

$$ 150\, \text{cm} = \dfrac{ 30\, \text{cm} \cdot d_2 }{ 2 } $$$$ 150\, \text{cm} \cdot 2 = 30\, \text{cm} \cdot d_2 $$$$ 300\, \text{cm} = 30\, \text{cm} \cdot d_2 $$$$ d_2 = \dfrac{ 300\, \text{cm} }{ 30\, \text{cm} } $$$$ d_2 = 10 $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $d_2 = 10\, \text{cm}^0$ and $d_1 = 30\, \text{cm}$ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 10 }{ 30\, \text{cm} } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 1 }{ 3 }\, \text{cm}^-1 $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 1 }{ 3 }\, \text{cm}^-1 \right) $$ $$ \frac{ \alpha }{ 2 } = 19.4712^o $$$$ \alpha = 19.4712^o \cdot 2 $$$$ \alpha = 38.9424^o $$

Rhombus Calculator