STEP 1: find side $ a $

To find side $ a $ use formula:

$$ d = \sqrt{ 2 } \cdot a $$

After substituting $d = 20.4\, \text{cm}$ we have:

$$ 20.4\, \text{cm} = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ 20.4\, \text{cm} }{ \sqrt{ 2 } } $$ $$ a \approx 14.425\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $a = 14.425\, \text{cm}$ and $s = 90.3\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ \left( 14.425\, \text{cm} \right)^{2} }{ 4 } = \left( 90.3\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 208.08\, \text{cm}^2 }{ 4 } = \left( 90.3\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + 52.02\, \text{cm}^2 = \left( 90.3\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 8154.09\, \text{cm}^2 - 52.02\, \text{cm}^2 $$ $$ h ^ {\,2} = 8102.07\, \text{cm}^2 $$ $$ h = \sqrt{ 8102.07\, \text{cm}^2 } $$$$ h = 90.0115\, \text{cm} $$

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