Find the side $ a $ of a pyramid if height $h = 8$ and slant height $s = 10$.
Answer
$a = 12$
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 8 $ and $ s = 10 $ we have:
$$ 8^2 + \frac{ a^2 }{ 4 } = 10^2 $$ $$ \frac{ a^2 }{ 4 } = 10^2 - 8^2 $$ $$ \frac{ a^2 }{ 4 } = 100 - 64 $$ $$ a^2 = 36 \cdot 4 $$ $$ a^2 = 144 $$ $$ a = \sqrt{ 144 } $$$$ a = 12 $$This page was created using
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