Find the side $ a $ of a pyramid if height $h = 6$ and lateral edge $e = 10$.
Answer
$a = 8 \sqrt{ 2 }$
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 = 6 $ and $ e = 10 $ we have:
$$ 6^2 + \frac{ d^2 }{ 4 } = 10^2 $$ $$ \frac{ d^2 }{ 4 } = 10^2 - 6^2 $$ $$ \frac{ d^2 }{ 4 } = 100 - 36 $$ $$ d^2 = 64 \cdot 4 $$ $$ d^2 = 256 $$ $$ d = \sqrt{ 256 } $$$$ d = 16 $$STEP 2: find side $ a $
To find side $ a $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ d = 16 $ we have:
$$ 16 = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ 16 }{ \sqrt{ 2 } } $$ $$ a = 8 \sqrt{ 2 } $$This page was created using
Pyramid Calculator