Question
Find the lateral edge $ e $ of a pyramid if side $a = 2\, \text{cm}$ and slant height $s = 1.619\, \text{cm}$.
Answer
$1.9029\, \text{cm}$
Explanation
To find lateral edge $ e $ use Pythagorean Theorem:
$$ s^2 + \frac{ a^2 }{ 4 } = e^2 $$After substituting $s = 1.619\, \text{cm}$ and $a = 2\, \text{cm}$ we have:
$$ \left( 1.619\, \text{cm} \right)^{2} + \frac{ \left( 2\, \text{cm} \right)^{2} }{ 4 }= e^2 $$ $$ 2.6212\, \text{cm}^2 + \frac{ 4\, \text{cm}^2 }{ 4 }= e^2 $$ $$ 2.6212\, \text{cm}^2 + 1\, \text{cm}^2 = e^2 $$ $$ e^2 = 3.6212\, \text{cm}^2 $$ $$ e = \sqrt{ 3.6212\, \text{cm}^2 } $$$$ e = 1.9029\, \text{cm} $$This page was created using
Pyramid Calculator