Find the height $ h $ of a pyramid if side $a = 22$ and slant height $s = 23$.
Answer
$h = 2 \sqrt{ 102 }$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 22 $ and $ s = 23 $ we have:
$$ h ^ {\,2} + \frac{ 22^2 }{ 4 } = 23^2 $$ $$ h ^ {\,2} + \frac{ 484 }{ 4 } = 23^2 $$ $$ h ^ {\,2} + 121 = 23^2 $$ $$ h ^ {\,2} = 529 - 121 $$ $$ h ^ {\,2} = 408 $$ $$ h = \sqrt{ 408 } $$$$ h = 2 \sqrt{ 102 } $$This page was created using
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