Find the slant height $ s $ of a pyramid if side $a = 7$ and height $h = 6$.
Answer
$s = \frac{\sqrt{ 193 }}{ 2 }$
Explanation
To find slant height $ s $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 6 $ and $ a = 7 $ we have:
$$ 6^2 + \frac{ 7^2 }{ 4 }= s^2 $$ $$ 36 + \frac{ 49 }{ 4 }= s^2 $$ $$ 36 + \frac{ 49 }{ 4 } = s^2 $$ $$ s^2 = \frac{ 193 }{ 4 } $$ $$ s = \sqrt{ \frac{ 193 }{ 4 } } $$$$ s = \frac{\sqrt{ 193 }}{ 2 } $$This page was created using
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