STEP 1: find side $ a $

To find side $ a $ use Pythagorean Theorem:

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

After substituting $h = 65\, \text{cm}$ and $s = 66\, \text{cm}$ we have:

$$ \left( 65\, \text{cm} \right)^{2} + \frac{ a^2 }{ 4 } = \left( 66\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = \left( 66\, \text{cm} \right)^{2} - \left( 65\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = 4356\, \text{cm}^2 - 4225\, \text{cm}^2 $$ $$ a^2 = 131\, \text{cm}^2 \cdot 4 $$ $$ a^2 = 524\, \text{cm}^2 $$ $$ a = \sqrt{ 524\, \text{cm}^2 } $$$$ a = 2 \sqrt{ 131 }\, \text{cm} $$

STEP 2: find base diagonal $ d $

To find base diagonal $ d $ use formula:

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

After substituting $a = 2 \sqrt{ 131 }\, \text{cm}$ we have:

$$ d = \sqrt{ 2 } \cdot 2 \sqrt{ 131 }\, \text{cm} $$ $$ d = 2 \sqrt{ 262 }\, \text{cm} $$

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