To find side $ a $ use Pythagorean Theorem:

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

After substituting $h = 10\, \text{cm}$ and $s = 12\, \text{cm}$ we have:

$$ \left( 10\, \text{cm} \right)^{2} + \frac{ a^2 }{ 4 } = \left( 12\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = \left( 12\, \text{cm} \right)^{2} - \left( 10\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = 144\, \text{cm}^2 - 100\, \text{cm}^2 $$ $$ a^2 = 44\, \text{cm}^2 \cdot 4 $$ $$ a^2 = 176\, \text{cm}^2 $$ $$ a = \sqrt{ 176\, \text{cm}^2 } $$$$ a = 4 \sqrt{ 11 }\, \text{cm} $$

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