Find the lateral edge $ e $ of a pyramid if side $a = 18$ and height $h = 4$.
Answer
$e = \sqrt{ 178 }$
Explanation
STEP 1: find base diagonal $ d $
To find base diagonal $ d $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ a = 18 $ we have:
$$ d = \sqrt{ 2 } \cdot 18 $$ $$ d = 18 \sqrt{ 2 } $$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 = 4 $ and $ d = 18 \sqrt{ 2 } $ we have:
$$ 4^2 + \frac{ \left(18 \sqrt{ 2 }\right)^2 }{ 4 }= e^2 $$ $$ 16 + \frac{ 648 }{ 4 }= e^2 $$ $$ 16 + 162 = e^2 $$ $$ e^2 = 178 $$ $$ e = \sqrt{ 178 } $$This page was created using
Pyramid Calculator