Find the base diagonal $ d $ of a pyramid if height $h = 65$ and slant height $s = 66$.
Answer
$d = 2 \sqrt{ 262 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 65 $ and $ s = 66 $ we have:
$$ 65^2 + \frac{ a^2 }{ 4 } = 66^2 $$ $$ \frac{ a^2 }{ 4 } = 66^2 - 65^2 $$ $$ \frac{ a^2 }{ 4 } = 4356 - 4225 $$ $$ a^2 = 131 \cdot 4 $$ $$ a^2 = 524 $$ $$ a = \sqrt{ 524 } $$$$ a = 2 \sqrt{ 131 } $$STEP 2: find base diagonal $ d $
To find base diagonal $ d $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ a = 2 \sqrt{ 131 } $ we have:
$$ d = \sqrt{ 2 } \cdot 2 \sqrt{ 131 } $$ $$ d = 2 \sqrt{ 262 } $$This page was created using
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