Find the height $ h $ of a pyramid if side $a = 6$ and slant height $s = 12$.
Answer
$h = 3 \sqrt{ 15 }$
Explanation
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 6 $ and $ s = 12 $ we have:
$$ h ^ {\,2} + \frac{ 6^2 }{ 4 } = 12^2 $$ $$ h ^ {\,2} + \frac{ 36 }{ 4 } = 12^2 $$ $$ h ^ {\,2} + 9 = 12^2 $$ $$ h ^ {\,2} = 144 - 9 $$ $$ h ^ {\,2} = 135 $$ $$ h = \sqrt{ 135 } $$$$ h = 3 \sqrt{ 15 } $$This page was created using
Pyramid Calculator