Find the base diagonal $ d $ of a pyramid if height $h = 1$ and lateral edge $e = 3$.
Answer
$d = 4 \sqrt{ 2 }$
Explanation
To find base diagonal $ d $ use Pythagorean Theorem:
$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$After substituting $ h = 1 $ and $ e = 3 $ we have:
$$ 1^2 + \frac{ d^2 }{ 4 } = 3^2 $$ $$ \frac{ d^2 }{ 4 } = 3^2 - 1^2 $$ $$ \frac{ d^2 }{ 4 } = 9 - 1 $$ $$ d^2 = 8 \cdot 4 $$ $$ d^2 = 32 $$ $$ d = \sqrt{ 32 } $$$$ d = 4 \sqrt{ 2 } $$This page was created using
Pyramid Calculator