Find the slant height $ s $ of a pyramid if side $a = 8$ and total surface $A = 304$.

$s = 15$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 8 $ we have:

$$ B = 8^2 $$ $$ B = 64 $$

STEP 2: find lateral surface $ L $

To find lateral surface $ L $ use formula:

$$ A = B + L $$

After substituting $ A = 304 $ and $ B = 64 $ we have:

$$ 304 = 64 + L $$ $$ L = 304 - 64 $$ $$ L = 240 $$

STEP 3: find slant height $ s $

To find slant height $ s $ use formula:

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

After substituting $ L = 240 $ and $ a = 8 $ we have:

$$ 240 = 2 \cdot 8 \cdot s $$$$ 240 = 16 \cdot s $$$$ s = \dfrac{ 240 }{ 16 } $$$$ s = 15 $$

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