Find the height $ h $ of a pyramid if side $a = 8$ and slant height $s = 13$.
Answer
$h = 3 \sqrt{ 17 }$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 8 $ and $ s = 13 $ we have:
$$ h ^ {\,2} + \frac{ 8^2 }{ 4 } = 13^2 $$ $$ h ^ {\,2} + \frac{ 64 }{ 4 } = 13^2 $$ $$ h ^ {\,2} + 16 = 13^2 $$ $$ h ^ {\,2} = 169 - 16 $$ $$ h ^ {\,2} = 153 $$ $$ h = \sqrt{ 153 } $$$$ h = 3 \sqrt{ 17 } $$This page was created using
Pyramid Calculator