Find the height $ h $ of a pyramid if side $a = 31.6$ and slant height $s = 39.6$.
Answer
$h = 36.3114$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 31.6 $ and $ s = 39.6 $ we have:
$$ h ^ {\,2} + \frac{ 31.6^2 }{ 4 } = 39.6^2 $$ $$ h ^ {\,2} + \frac{ 998.56 }{ 4 } = 39.6^2 $$ $$ h ^ {\,2} + 249.64 = 39.6^2 $$ $$ h ^ {\,2} = 1568.16 - 249.64 $$ $$ h ^ {\,2} = 1318.52 $$ $$ h = \sqrt{ 1318.52 } $$$$ h = 36.3114 $$This page was created using
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