STEP 1: find side $ a $

To find side $ a $ use formula:

$$ r = \dfrac{ a }{ 2 } $$

After substituting $r = 45.822\, \text{cm}$ we have:

$$ 45.822\, \text{cm} = \dfrac{ a }{ 2 } $$ $$ a = 45.822\, \text{cm} \cdot 2 $$ $$ a = 91.644\, \text{cm} $$

STEP 2: find lateral edge $ e $

To find lateral edge $ e $ use Pythagorean Theorem:

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

After substituting $s = 68.479\, \text{cm}$ and $a = 91.644\, \text{cm}$ we have:

$$ \left( 68.479\, \text{cm} \right)^{2} + \frac{ \left( 91.644\, \text{cm} \right)^{2} }{ 4 }= e^2 $$ $$ 4689.3734\, \text{cm}^2 + \frac{ 8398.6227\, \text{cm}^2 }{ 4 }= e^2 $$ $$ 4689.3734\, \text{cm}^2 + 2099.6557\, \text{cm}^2 = e^2 $$ $$ e^2 = 6789.0291\, \text{cm}^2 $$ $$ e = \sqrt{ 6789.0291\, \text{cm}^2 } $$$$ e = 82.3956\, \text{cm} $$

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