Find the height $ h $ of a pyramid if slant height $s = 68.479$ and base radius $r = 45.822$.

$h = 50.8893$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ r = \dfrac{ a }{ 2 } $$

After substituting $ r = 45.822 $ we have:

$$ 45.822 = \dfrac{ a }{ 2 } $$ $$ a = 45.822 \cdot 2 $$ $$ a = 91.644 $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $ a = 91.644 $ and $ s = 68.479 $ we have:

$$ h ^ {\,2} + \frac{ 91.644^2 }{ 4 } = 68.479^2 $$ $$ h ^ {\,2} + \frac{ 8398.6227 }{ 4 } = 68.479^2 $$ $$ h ^ {\,2} + 2099.6557 = 68.479^2 $$ $$ h ^ {\,2} = 4689.3734 - 2099.6557 $$ $$ h ^ {\,2} = 2589.7178 $$ $$ h = \sqrt{ 2589.7178 } $$$$ h = 50.8893 $$

Pyramid Calculator