Find the side $ a $ of a pyramid if height $h = 10$ and slant height $s = 12$.
Answer
$a = 4 \sqrt{ 11 }$
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 10 $ and $ s = 12 $ we have:
$$ 10^2 + \frac{ a^2 }{ 4 } = 12^2 $$ $$ \frac{ a^2 }{ 4 } = 12^2 - 10^2 $$ $$ \frac{ a^2 }{ 4 } = 144 - 100 $$ $$ a^2 = 44 \cdot 4 $$ $$ a^2 = 176 $$ $$ a = \sqrt{ 176 } $$$$ a = 4 \sqrt{ 11 } $$This page was created using
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