STEP 1: find side $ a $

To find side $ a $ use formula:

After substituting $B = 16\, \text{cm}$ we have:

$$ B = a^2 $$ $$ a^2 = 16\, \text{cm} $$ $$ a = \sqrt{ 16\, \text{cm} } $$ $$ a = 4 $$

STEP 2: find lateral surface $ L $

To find lateral surface $ L $ use formula:

$$ A = B + L $$

After substituting $A = 800\, \text{cm}$ and $B = 16\, \text{cm}$ we have:

$$ 800\, \text{cm} = 16\, \text{cm} + L $$ $$ L = 800\, \text{cm} - 16\, \text{cm} $$ $$ L = 784\, \text{cm} $$

STEP 3: find slant height $ s $

To find slant height $ s $ use formula:

$$ L = 2 \cdot a \cdot s $$

After substituting $L = 784\, \text{cm}$ and $a = 4\, \text{cm}^0$ we have:

$$ 784\, \text{cm} = 2 \cdot 4 \cdot s $$$$ 784\, \text{cm} = 8 \cdot s $$$$ s = \dfrac{ 784\, \text{cm} }{ 8 } $$$$ s = 98\, \text{cm} $$

STEP 4: find height $ h $

To find height $ h $ use Pythagorean Theorem:

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

After substituting $a = 4\, \text{cm}^0$ and $s = 98\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ 4 }{ 4 } = \left( 98\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 16 }{ 4 } = \left( 98\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + 4 = \left( 98\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 9604\, \text{cm}^2 - 4 $$ $$ h ^ {\,2} = 9600\, \text{cm}^2 $$ $$ h = \sqrt{ 9600\, \text{cm}^2 } $$$$ h = 40 \sqrt{ 6 }\, \text{cm} $$

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