Find the height $ h $ of a pyramid if side $a = 9$ and slant height $s = 13$.
Answer
$h = \frac{\sqrt{ 595 }}{ 2 }$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 9 $ and $ s = 13 $ we have:
$$ h ^ {\,2} + \frac{ 9^2 }{ 4 } = 13^2 $$ $$ h ^ {\,2} + \frac{ 81 }{ 4 } = 13^2 $$ $$ h ^ {\,2} + \frac{ 81 }{ 4 } = 13^2 $$ $$ h ^ {\,2} = 169 - \frac{ 81 }{ 4 } $$ $$ h ^ {\,2} = \frac{ 595 }{ 4 } $$ $$ h = \sqrt{ \frac{ 595 }{ 4 } } $$$$ h = \frac{\sqrt{ 595 }}{ 2 } $$This page was created using
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