Find the side $ a $ of a pyramid if height $h = 4$ and lateral edge $e = 5$.
Answer
$a = 3 \sqrt{ 2 }$
Explanation
STEP 1: find base diagonal $ d $
To find base diagonal $ d $ use Pythagorean Theorem:
$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$After substituting $ h = 4 $ and $ e = 5 $ we have:
$$ 4^2 + \frac{ d^2 }{ 4 } = 5^2 $$ $$ \frac{ d^2 }{ 4 } = 5^2 - 4^2 $$ $$ \frac{ d^2 }{ 4 } = 25 - 16 $$ $$ d^2 = 9 \cdot 4 $$ $$ d^2 = 36 $$ $$ d = \sqrt{ 36 } $$$$ d = 6 $$STEP 2: find side $ a $
To find side $ a $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ d = 6 $ we have:
$$ 6 = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ 6 }{ \sqrt{ 2 } } $$ $$ a = 3 \sqrt{ 2 } $$This page was created using
Pyramid Calculator