Find the side $ a $ of a pyramid if height $h = 24$ and lateral edge $e = 26$.

$a = 10 \sqrt{ 2 }$

STEP 1: find base diagonal $ d $

To find base diagonal $ d $ use Pythagorean Theorem:

$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$

After substituting $ h = 24 $ and $ e = 26 $ we have:

$$ 24^2 + \frac{ d^2 }{ 4 } = 26^2 $$ $$ \frac{ d^2 }{ 4 } = 26^2 - 24^2 $$ $$ \frac{ d^2 }{ 4 } = 676 - 576 $$ $$ d^2 = 100 \cdot 4 $$ $$ d^2 = 400 $$ $$ d = \sqrt{ 400 } $$$$ d = 20 $$

STEP 2: find side $ a $

To find side $ a $ use formula:

$$ d = \sqrt{ 2 } \cdot a $$

After substituting $ d = 20 $ we have:

$$ 20 = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ 20 }{ \sqrt{ 2 } } $$ $$ a = 10 \sqrt{ 2 } $$

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