STEP 1: find side $ a $

To find side $ a $ use formula:

$$ P = 4 \cdot a $$

After substituting $P = 32\, \text{cm}$ we have:

$$ 32\, \text{cm} = 4 \cdot a $$ $$ a = \dfrac{ 32\, \text{cm} }{ 4 } $$ $$ a = 8\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $a = 8\, \text{cm}$, $a = 8\, \text{cm}$ and $\alpha = 45^o$ we have:

$$ A = \dfrac{ 8\, \text{cm} \cdot 8\, \text{cm} \cdot \sin( 45^o ) }{ 1 } $$ $$ A = \dfrac{ 8\, \text{cm} \cdot 8\, \text{cm} \cdot \frac{\sqrt{ 2 }}{ 2 } }{ 1 } $$ $$ A = \dfrac{ 64\, \text{cm}^2 \cdot \frac{\sqrt{ 2 }}{ 2 } }{ 1 } $$ $$ A = \dfrac{ 32 \sqrt{ 2 }\, \text{cm}^2 }{ 1 } $$ $$ A = 32 \sqrt{ 2 }\, \text{cm}^2 $$

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