STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \alpha + \beta = 90^o $$

After substituting $ \beta = 58^o $ we have:

$$ \alpha + 58^o = 90^o $$ $$ \alpha = 90^o - 58^o $$ $$ \alpha = 32^o $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = \dfrac{ a \cdot a \cdot \sin( \alpha ) }{ 1 } $$

After substituting $a = 2\, \text{cm}$, $a = 2\, \text{cm}$ and $\alpha = 32^o$ we have:

$$ A = \dfrac{ 2\, \text{cm} \cdot 2\, \text{cm} \cdot \sin( 32^o ) }{ 1 } $$ $$ A = \dfrac{ 2\, \text{cm} \cdot 2\, \text{cm} \cdot 0.5299 }{ 1 } $$ $$ A = \dfrac{ 4\, \text{cm}^2 \cdot 0.5299 }{ 1 } $$ $$ A = \dfrac{ 2.1197\, \text{cm}^2 }{ 1 } $$ $$ A \approx 2.1197\, \text{cm}^2 $$

Rhombus Calculator