STEP 1: find base diagonal $ d $

To find base diagonal $ d $ use formula:

$$ d = \sqrt{ 2 } \cdot a $$

After substituting $a = 210\, \text{cm}$ we have:

$$ d = \sqrt{ 2 } \cdot 210\, \text{cm} $$ $$ d = 210 \sqrt{ 2 }\, \text{cm} $$

STEP 2: find lateral edge $ e $

To find lateral edge $ e $ use Pythagorean Theorem:

$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$

After substituting $h = 45\, \text{cm}$ and $d = 210 \sqrt{ 2 }\, \text{cm}$ we have:

$$ \left( 45\, \text{cm} \right)^{2} + \frac{ \left( 210 \sqrt{ 2 }\, \text{cm} \right)^{2} }{ 4 }= e^2 $$ $$ 2025\, \text{cm}^2 + \frac{ 88200\, \text{cm}^2 }{ 4 }= e^2 $$ $$ 2025\, \text{cm}^2 + 22050\, \text{cm}^2 = e^2 $$ $$ e^2 = 24075\, \text{cm}^2 $$ $$ e = \sqrt{ 24075\, \text{cm}^2 } $$$$ e = 15 \sqrt{ 107 }\, \text{cm} $$

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