To find slant height $ s $ use Pythagorean Theorem:

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

After substituting $h = 6\, \text{cm}$ and $a = 7\, \text{cm}$ we have:

$$ \left( 6\, \text{cm} \right)^{2} + \frac{ \left( 7\, \text{cm} \right)^{2} }{ 4 }= s^2 $$ $$ 36\, \text{cm}^2 + \frac{ 49\, \text{cm}^2 }{ 4 }= s^2 $$ $$ 36\, \text{cm}^2 + \frac{ 49 }{ 4 }\, \text{cm}^2 = s^2 $$ $$ s^2 = \frac{ 193 }{ 4 }\, \text{cm}^2 $$ $$ s = \sqrt{ \frac{ 193 }{ 4 }\, \text{cm}^2 } $$$$ s = \frac{\sqrt{ 193 }}{ 2 }\, \text{cm} $$

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