STEP 1: find base diagonal $ d $

To find base diagonal $ d $ use formula:

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

After substituting $a = 1\, \text{cm}$ we have:

$$ d = \sqrt{ 2 } \cdot 1\, \text{cm} $$ $$ d = \sqrt{ 2 }\, \text{cm} $$

STEP 2: find lateral edge $ e $

To find lateral edge $ e $ use Pythagorean Theorem:

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

After substituting $h = 1\, \text{cm}$ and $d = \sqrt{ 2 }\, \text{cm}$ we have:

$$ \left( 1\, \text{cm} \right)^{2} + \frac{ \left( \sqrt{ 2 }\, \text{cm} \right)^{2} }{ 4 }= e^2 $$ $$ 1\, \text{cm}^2 + \frac{ 2\, \text{cm}^2 }{ 4 }= e^2 $$ $$ 1\, \text{cm}^2 + \frac{ 1 }{ 2 }\, \text{cm}^2 = e^2 $$ $$ e^2 = \frac{ 3 }{ 2 }\, \text{cm}^2 $$ $$ e = \sqrt{ \frac{ 3 }{ 2 }\, \text{cm}^2 } $$$$ e = \frac{\sqrt{ 6 }}{ 2 }\, \text{cm} $$

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