Find the slant height $ s $ of a pyramid if height $h = 10$ and base area $B = 25$.
Answer
$s = \frac{ 5 \sqrt{ 17}}{ 2 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
After substituting $ B = 25 $ we have:
$$ B = a^2 $$ $$ a^2 = 25 $$ $$ a = \sqrt{ 25 } $$ $$ a = 5 $$STEP 2: find slant height $ s $
To find slant height $ s $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 10 $ and $ a = 5 $ we have:
$$ 10^2 + \frac{ 5^2 }{ 4 }= s^2 $$ $$ 100 + \frac{ 25 }{ 4 }= s^2 $$ $$ 100 + \frac{ 25 }{ 4 } = s^2 $$ $$ s^2 = \frac{ 425 }{ 4 } $$ $$ s = \sqrt{ \frac{ 425 }{ 4 } } $$$$ s = \frac{ 5 \sqrt{ 17}}{ 2 } $$This page was created using
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