Question
Find the slant height $ s $ of a pyramid if side $a = 28\, \text{mm}$ and height $h = 20\, \text{mm}$.
Answer
$2 \sqrt{ 149 }\, \text{mm}$
Explanation
To find slant height $ s $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $h = 20\, \text{mm}$ and $a = 28\, \text{mm}$ we have:
$$ \left( 20\, \text{mm} \right)^{2} + \frac{ \left( 28\, \text{mm} \right)^{2} }{ 4 }= s^2 $$ $$ 400\, \text{mm}^2 + \frac{ 784\, \text{mm}^2 }{ 4 }= s^2 $$ $$ 400\, \text{mm}^2 + 196\, \text{mm}^2 = s^2 $$ $$ s^2 = 596\, \text{mm}^2 $$ $$ s = \sqrt{ 596\, \text{mm}^2 } $$$$ s = 2 \sqrt{ 149 }\, \text{mm} $$This page was created using
Pyramid Calculator