Find the height $ h $ of a pyramid if side $a = 4$ and slant height $s = 13$.
Answer
$h = \sqrt{ 165 }$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 4 $ and $ s = 13 $ we have:
$$ h ^ {\,2} + \frac{ 4^2 }{ 4 } = 13^2 $$ $$ h ^ {\,2} + \frac{ 16 }{ 4 } = 13^2 $$ $$ h ^ {\,2} + 4 = 13^2 $$ $$ h ^ {\,2} = 169 - 4 $$ $$ h ^ {\,2} = 165 $$ $$ h = \sqrt{ 165 } $$This page was created using
Pyramid Calculator