STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $a = 10\, \text{cm}$ we have:

$$ B = \left( 10\, \text{cm} \right)^{2} $$ $$ B = 100\, \text{cm}^2 $$

STEP 2: find lateral surface $ L $

To find lateral surface $ L $ use formula:

$$ A = B + L $$

After substituting $A = 214.5\, \text{cm}$ and $B = 100\, \text{cm}^2$ we have:

$$ 214.5\, \text{cm} = 100\, \text{cm}^2 + L $$ $$ L = 214.5\, \text{cm} - 100\, \text{cm}^2 $$ $$ L = 114.5\, \text{cm} $$

STEP 3: find slant height $ s $

To find slant height $ s $ use formula:

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

After substituting $L = 114.5\, \text{cm}$ and $a = 10\, \text{cm}$ we have:

$$ 114.5\, \text{cm} = 2 \cdot 10\, \text{cm} \cdot s $$$$ 114.5\, \text{cm} = 20\, \text{cm} \cdot s $$$$ s = \dfrac{ 114.5\, \text{cm} }{ 20\, \text{cm} } $$$$ s = 5.725 $$

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