Question
Find the slant height $ s $ of a pyramid if side $a = 8\, \text{cm}$ and height $h = 10\, \text{cm}$.
Answer
$2 \sqrt{ 29 }\, \text{cm}$
Explanation
To find slant height $ s $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $h = 10\, \text{cm}$ and $a = 8\, \text{cm}$ we have:
$$ \left( 10\, \text{cm} \right)^{2} + \frac{ \left( 8\, \text{cm} \right)^{2} }{ 4 }= s^2 $$ $$ 100\, \text{cm}^2 + \frac{ 64\, \text{cm}^2 }{ 4 }= s^2 $$ $$ 100\, \text{cm}^2 + 16\, \text{cm}^2 = s^2 $$ $$ s^2 = 116\, \text{cm}^2 $$ $$ s = \sqrt{ 116\, \text{cm}^2 } $$$$ s = 2 \sqrt{ 29 }\, \text{cm} $$This page was created using
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