Find the slant height $ s $ of a pyramid if side $a = 10$ and total surface $A = 214.5$.

$s = 5.725$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 10 $ we have:

$$ B = 10^2 $$ $$ B = 100 $$

STEP 2: find lateral surface $ L $

To find lateral surface $ L $ use formula:

$$ A = B + L $$

After substituting $ A = 214.5 $ and $ B = 100 $ we have:

$$ 214.5 = 100 + L $$ $$ L = 214.5 - 100 $$ $$ L = 114.5 $$

STEP 3: find slant height $ s $

To find slant height $ s $ use formula:

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

After substituting $ L = 114.5 $ and $ a = 10 $ we have:

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

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