Find the height $ h $ of a pyramid if side $a = 26$ and lateral edge $e = 24$.
Answer
$h = \sqrt{ 238 }$
Explanation
STEP 1: find base diagonal $ d $
To find base diagonal $ d $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ a = 26 $ we have:
$$ d = \sqrt{ 2 } \cdot 26 $$ $$ d = 26 \sqrt{ 2 } $$STEP 2: find height $ h $
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$After substituting $ d = 26 \sqrt{ 2 } $ and $ e = 24 $ we have:
$$ h ^ {\,2} + \frac{ \left(26 \sqrt{ 2 }\right)^2 }{ 4 } = 24^2 $$ $$ h ^ {\,2} + \frac{ 1352 }{ 4 } = 24^2 $$ $$ h ^ {\,2} + 338 = 24^2 $$ $$ h ^ {\,2} = 576 - 338 $$ $$ h ^ {\,2} = 238 $$ $$ h = \sqrt{ 238 } $$This page was created using
Pyramid Calculator