Question
Find the slant height $ s $ of a pyramid if side $a = 2\, \text{cm}$ and height $h = 2\, \text{cm}$.
Answer
$\sqrt{ 5 }\, \text{cm}$
Explanation
To find slant height $ s $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $h = 2\, \text{cm}$ and $a = 2\, \text{cm}$ we have:
$$ \left( 2\, \text{cm} \right)^{2} + \frac{ \left( 2\, \text{cm} \right)^{2} }{ 4 }= s^2 $$ $$ 4\, \text{cm}^2 + \frac{ 4\, \text{cm}^2 }{ 4 }= s^2 $$ $$ 4\, \text{cm}^2 + 1\, \text{cm}^2 = s^2 $$ $$ s^2 = 5\, \text{cm}^2 $$ $$ s = \sqrt{ 5\, \text{cm}^2 } $$$$ s = \sqrt{ 5 }\, \text{cm} $$This page was created using
Pyramid Calculator