STEP 1: find side $ a $

To find side $ a $ use formula:

After substituting $B = 1.5\, \text{cm}$ we have:

$$ B = a^2 $$ $$ a^2 = 1.5\, \text{cm} $$ $$ a = \sqrt{ 1.5\, \text{cm} } $$$$ a \approx 1.2247 $$

STEP 2: find base diagonal $ d $

To find base diagonal $ d $ use formula:

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

After substituting $a = 1.2247\, \text{cm}^0$ we have:

$$ d = \sqrt{ 2 } \cdot 1.2247 $$ $$ d \approx 1.7321 $$

STEP 3: find height $ h $

To find height $ h $ use Pythagorean Theorem:

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

After substituting $d = 1.7321\, \text{cm}^0$ and $e = 10\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ 1.7321 }{ 4 } = \left( 10\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 3 }{ 4 } = \left( 10\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + 0.75 = \left( 10\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 100\, \text{cm}^2 - 0.75 $$ $$ h ^ {\,2} = 99.25\, \text{cm}^2 $$ $$ h = \sqrt{ 99.25\, \text{cm}^2 } $$$$ h = 9.9624\, \text{cm} $$

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