Find the side $ a $ of a pyramid if height $h = 13$ and slant height $s = 15$.
Answer
$a = 4 \sqrt{ 14 }$
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 13 $ and $ s = 15 $ we have:
$$ 13^2 + \frac{ a^2 }{ 4 } = 15^2 $$ $$ \frac{ a^2 }{ 4 } = 15^2 - 13^2 $$ $$ \frac{ a^2 }{ 4 } = 225 - 169 $$ $$ a^2 = 56 \cdot 4 $$ $$ a^2 = 224 $$ $$ a = \sqrt{ 224 } $$$$ a = 4 \sqrt{ 14 } $$This page was created using
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