Find the slant height $ s $ of a pyramid if side $a = 15$ and total surface $A = 525$.

$s = 10$

STEP 1: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $ a = 15 $ we have:

$$ B = 15^2 $$ $$ B = 225 $$

STEP 2: find lateral surface $ L $

To find lateral surface $ L $ use formula:

$$ A = B + L $$

After substituting $ A = 525 $ and $ B = 225 $ we have:

$$ 525 = 225 + L $$ $$ L = 525 - 225 $$ $$ L = 300 $$

STEP 3: find slant height $ s $

To find slant height $ s $ use formula:

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

After substituting $ L = 300 $ and $ a = 15 $ we have:

$$ 300 = 2 \cdot 15 \cdot s $$$$ 300 = 30 \cdot s $$$$ s = \dfrac{ 300 }{ 30 } $$$$ s = 10 $$

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