Find the height $ h $ of a pyramid if side $a = 12$ and slant height $s = 18$.
Answer
$h = 12 \sqrt{ 2 }$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 12 $ and $ s = 18 $ we have:
$$ h ^ {\,2} + \frac{ 12^2 }{ 4 } = 18^2 $$ $$ h ^ {\,2} + \frac{ 144 }{ 4 } = 18^2 $$ $$ h ^ {\,2} + 36 = 18^2 $$ $$ h ^ {\,2} = 324 - 36 $$ $$ h ^ {\,2} = 288 $$ $$ h = \sqrt{ 288 } $$$$ h = 12 \sqrt{ 2 } $$This page was created using
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