To find height $ h $ use Pythagorean Theorem:

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

After substituting $a = 6\, \text{cm}$ and $s = 19\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ \left( 6\, \text{cm} \right)^{2} }{ 4 } = \left( 19\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 36\, \text{cm}^2 }{ 4 } = \left( 19\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + 9\, \text{cm}^2 = \left( 19\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 361\, \text{cm}^2 - 9\, \text{cm}^2 $$ $$ h ^ {\,2} = 352\, \text{cm}^2 $$ $$ h = \sqrt{ 352\, \text{cm}^2 } $$$$ h = 4 \sqrt{ 22 }\, \text{cm} $$

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