STEP 1: find side $ a $

To find side $ a $ use Pythagorean Theorem:

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

After substituting $h = 16\, \text{cm}$ and $s = 20\, \text{cm}$ we have:

$$ \left( 16\, \text{cm} \right)^{2} + \frac{ a^2 }{ 4 } = \left( 20\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = \left( 20\, \text{cm} \right)^{2} - \left( 16\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = 400\, \text{cm}^2 - 256\, \text{cm}^2 $$ $$ a^2 = 144\, \text{cm}^2 \cdot 4 $$ $$ a^2 = 576\, \text{cm}^2 $$ $$ a = \sqrt{ 576\, \text{cm}^2 } $$$$ a = 24\, \text{cm} $$

STEP 2: find lateral edge $ e $

To find lateral edge $ e $ use Pythagorean Theorem:

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

After substituting $s = 20\, \text{cm}$ and $a = 24\, \text{cm}$ we have:

$$ \left( 20\, \text{cm} \right)^{2} + \frac{ \left( 24\, \text{cm} \right)^{2} }{ 4 }= e^2 $$ $$ 400\, \text{cm}^2 + \frac{ 576\, \text{cm}^2 }{ 4 }= e^2 $$ $$ 400\, \text{cm}^2 + 144\, \text{cm}^2 = e^2 $$ $$ e^2 = 544\, \text{cm}^2 $$ $$ e = \sqrt{ 544\, \text{cm}^2 } $$$$ e = 4 \sqrt{ 34 }\, \text{cm} $$

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