Find the slant height $ s $ of a pyramid if side $a = 72$ and height $h = 20$.
Answer
$s = 4 \sqrt{ 106 }$
Explanation
To find slant height $ s $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 20 $ and $ a = 72 $ we have:
$$ 20^2 + \frac{ 72^2 }{ 4 }= s^2 $$ $$ 400 + \frac{ 5184 }{ 4 }= s^2 $$ $$ 400 + 1296 = s^2 $$ $$ s^2 = 1696 $$ $$ s = \sqrt{ 1696 } $$$$ s = 4 \sqrt{ 106 } $$This page was created using
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