Find the lateral edge $ e $ of a pyramid if side $a = 210$ and height $h = 45$.
Answer
$e = 15 \sqrt{ 107 }$
Explanation
STEP 1: find base diagonal $ d $
To find base diagonal $ d $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ a = 210 $ we have:
$$ d = \sqrt{ 2 } \cdot 210 $$ $$ d = 210 \sqrt{ 2 } $$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 = 45 $ and $ d = 210 \sqrt{ 2 } $ we have:
$$ 45^2 + \frac{ \left(210 \sqrt{ 2 }\right)^2 }{ 4 }= e^2 $$ $$ 2025 + \frac{ 88200 }{ 4 }= e^2 $$ $$ 2025 + 22050 = e^2 $$ $$ e^2 = 24075 $$ $$ e = \sqrt{ 24075 } $$$$ e = 15 \sqrt{ 107 } $$This page was created using
Pyramid Calculator