Find the slant height $ s $ of a pyramid if side $a = 200$ and lateral edge $e = 400$.
Answer
$s = 100 \sqrt{ 15 }$
Explanation
To find slant height $ s $ use Pythagorean Theorem:
$$ s^2 + \frac{ a^2 }{ 4 } = e^2 $$After substituting $ a = 200 $ and $ e = 400 $ we have:
$$ s ^ {\,2} + \frac{ 200^2 }{ 4 } = 400^2 $$ $$ s ^ {\,2} + \frac{ 40000 }{ 4 } = 400^2 $$ $$ s ^ {\,2} + 10000 = 400^2 $$ $$ s ^ {\,2} = 160000 - 10000 $$ $$ s ^ {\,2} = 150000 $$ $$ s = \sqrt{ 150000 } $$$$ s = 100 \sqrt{ 15 } $$This page was created using
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