STEP 1: find side $ a $

To find side $ a $ use formula:

$$ P = 4 \cdot a $$

After substituting $P = 58\, \text{cm}$ we have:

$$ 58\, \text{cm} = 4 \cdot a $$ $$ a = \dfrac{ 58\, \text{cm} }{ 4 } $$ $$ a = \frac{ 29 }{ 2 }\, \text{cm} $$

STEP 2: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$

After substituting $d_1 = 10\, \text{cm}$ and $a = \dfrac{ 29 }{ 2 }\, \text{cm}$ we have:

$$ \left( 10\, \text{cm} \right)^{2} + d_2^2 = 4 \cdot \left( \frac{ 29 }{ 2 }\, \text{cm} \right)^{2} $$ $$ 100\, \text{cm}^2 + d_2^2 = 841\, \text{cm}^2 $$ $$ d_2^2 = 841\, \text{cm}^2 - 100\, \text{cm}^2 $$ $$ d_2^2 = 741\, \text{cm}^2 $$ $$ d_2 = \sqrt{ 741\, \text{cm}^2 } $$$$ d_2 = \sqrt{ 741 }\, \text{cm} $$

STEP 3: find area $ A $

To find area $ A $ use formula:

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

After substituting $d_1 = 10\, \text{cm}$ and $d_2 = \sqrt{ 741 }\, \text{cm}$ we have:

$$ A = \dfrac{ 10\, \text{cm} \cdot \sqrt{ 741 }\, \text{cm} }{ 2 }$$$$ A = \dfrac{ 10 \sqrt{ 741 }\, \text{cm}^2 }{ 2 } $$$$ A = 5 \sqrt{ 741 }\, \text{cm}^2 $$

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