To find height $ h $ use Pythagorean Theorem:

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

After substituting $a = 31.6\, \text{cm}$ and $s = 39.6\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ \left( 31.6\, \text{cm} \right)^{2} }{ 4 } = \left( 39.6\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 998.56\, \text{cm}^2 }{ 4 } = \left( 39.6\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + 249.64\, \text{cm}^2 = \left( 39.6\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 1568.16\, \text{cm}^2 - 249.64\, \text{cm}^2 $$ $$ h ^ {\,2} = 1318.52\, \text{cm}^2 $$ $$ h = \sqrt{ 1318.52\, \text{cm}^2 } $$$$ h = 36.3114\, \text{cm} $$

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