To find slant height $ s $ use Pythagorean Theorem:

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

After substituting $a = 200\, \text{cm}$ and $e = 400\, \text{cm}$ we have:

$$ s ^ {\,2} + \frac{ \left( 200\, \text{cm} \right)^{2} }{ 4 } = \left( 400\, \text{cm} \right)^{2} $$ $$ s ^ {\,2} + \frac{ 40000\, \text{cm}^2 }{ 4 } = \left( 400\, \text{cm} \right)^{2} $$ $$ s ^ {\,2} + 10000\, \text{cm}^2 = \left( 400\, \text{cm} \right)^{2} $$ $$ s ^ {\,2} = 160000\, \text{cm}^2 - 10000\, \text{cm}^2 $$ $$ s ^ {\,2} = 150000\, \text{cm}^2 $$ $$ s = \sqrt{ 150000\, \text{cm}^2 } $$$$ s = 100 \sqrt{ 15 }\, \text{cm} $$

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