Find the height $ h $ of a pyramid if side $a = 6$ and slant height $s = 19$.
Answer
$h = 4 \sqrt{ 22 }$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 6 $ and $ s = 19 $ we have:
$$ h ^ {\,2} + \frac{ 6^2 }{ 4 } = 19^2 $$ $$ h ^ {\,2} + \frac{ 36 }{ 4 } = 19^2 $$ $$ h ^ {\,2} + 9 = 19^2 $$ $$ h ^ {\,2} = 361 - 9 $$ $$ h ^ {\,2} = 352 $$ $$ h = \sqrt{ 352 } $$$$ h = 4 \sqrt{ 22 } $$This page was created using
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