Find the lateral edge $ e $ of a pyramid if side $a = 1$ and height $h = 1$.
Answer
$e = \frac{\sqrt{ 6 }}{ 2 }$
Explanation
STEP 1: find base diagonal $ d $
To find base diagonal $ d $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ a = 1 $ we have:
$$ d = \sqrt{ 2 } \cdot 1 $$ $$ d = \sqrt{ 2 } $$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 = 1 $ and $ d = \sqrt{ 2 } $ we have:
$$ 1^2 + \frac{ \left( \sqrt{ 2 } \right)^{ 2 } }{ 4 }= e^2 $$ $$ 1 + \frac{ 2 }{ 4 }= e^2 $$ $$ 1 + \frac{ 1 }{ 2 } = e^2 $$ $$ e^2 = \frac{ 3 }{ 2 } $$ $$ e = \sqrt{ \frac{ 3 }{ 2 } } $$$$ e = \frac{\sqrt{ 6 }}{ 2 } $$This page was created using
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