Find the lateral edge $ e $ of a pyramid if side $a = 20$ and height $h = 10.5$.
Answer
$e = 17.6139$
Explanation
STEP 1: find base diagonal $ d $
To find base diagonal $ d $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ a = 20 $ we have:
$$ d = \sqrt{ 2 } \cdot 20 $$ $$ d = 20 \sqrt{ 2 } $$STEP 2: find lateral edge $ e $
To find lateral edge $ e $ use Pythagorean Theorem:
$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$After substituting $ h = 10.5 $ and $ d = 20 \sqrt{ 2 } $ we have:
$$ 10.5^2 + \frac{ \left(20 \sqrt{ 2 }\right)^2 }{ 4 }= e^2 $$ $$ 110.25 + \frac{ 800 }{ 4 }= e^2 $$ $$ 110.25 + 200 = e^2 $$ $$ e^2 = 310.25 $$ $$ e = \sqrt{ 310.25 } $$$$ e = 17.6139 $$This page was created using
Pyramid Calculator