To find slant height $ s $ use Pythagorean Theorem:

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

After substituting $a = 16\, \text{cm}$ and $e = 17\, \text{cm}$ we have:

$$ s ^ {\,2} + \frac{ \left( 16\, \text{cm} \right)^{2} }{ 4 } = \left( 17\, \text{cm} \right)^{2} $$ $$ s ^ {\,2} + \frac{ 256\, \text{cm}^2 }{ 4 } = \left( 17\, \text{cm} \right)^{2} $$ $$ s ^ {\,2} + 64\, \text{cm}^2 = \left( 17\, \text{cm} \right)^{2} $$ $$ s ^ {\,2} = 289\, \text{cm}^2 - 64\, \text{cm}^2 $$ $$ s ^ {\,2} = 225\, \text{cm}^2 $$ $$ s = \sqrt{ 225\, \text{cm}^2 } $$$$ s = 15\, \text{cm} $$

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