Find the height $ h $ of a pyramid if side $a = 2$ and slant height $s = 11$.
Answer
$h = 2 \sqrt{ 30 }$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 2 $ and $ s = 11 $ we have:
$$ h ^ {\,2} + \frac{ 2^2 }{ 4 } = 11^2 $$ $$ h ^ {\,2} + \frac{ 4 }{ 4 } = 11^2 $$ $$ h ^ {\,2} + 1 = 11^2 $$ $$ h ^ {\,2} = 121 - 1 $$ $$ h ^ {\,2} = 120 $$ $$ h = \sqrt{ 120 } $$$$ h = 2 \sqrt{ 30 } $$This page was created using
Pyramid Calculator