To find height $ h $ use Pythagorean Theorem:

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

After substituting $a = 3\, \text{cm}$ and $s = 3\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ \left( 3\, \text{cm} \right)^{2} }{ 4 } = \left( 3\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 9\, \text{cm}^2 }{ 4 } = \left( 3\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 9 }{ 4 }\, \text{cm}^2 = \left( 3\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 9\, \text{cm}^2 - \frac{ 9 }{ 4 }\, \text{cm}^2 $$ $$ h ^ {\,2} = \frac{ 27 }{ 4 }\, \text{cm}^2 $$ $$ h = \sqrt{ \frac{ 27 }{ 4 }\, \text{cm}^2 } $$$$ h = \frac{ 3 \sqrt{ 3}}{ 2 }\, \text{cm} $$

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