Find the height $ h $ of a pyramid if side $a = 8$ and lateral edge $e = 9$.
Answer
$h = 7$
Explanation
STEP 1: find base diagonal $ d $
To find base diagonal $ d $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ a = 8 $ we have:
$$ d = \sqrt{ 2 } \cdot 8 $$ $$ d = 8 \sqrt{ 2 } $$STEP 2: find height $ h $
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$After substituting $ d = 8 \sqrt{ 2 } $ and $ e = 9 $ we have:
$$ h ^ {\,2} + \frac{ \left(8 \sqrt{ 2 }\right)^2 }{ 4 } = 9^2 $$ $$ h ^ {\,2} + \frac{ 128 }{ 4 } = 9^2 $$ $$ h ^ {\,2} + 32 = 9^2 $$ $$ h ^ {\,2} = 81 - 32 $$ $$ h ^ {\,2} = 49 $$ $$ h = \sqrt{ 49 } $$$$ h = 7 $$This page was created using
Pyramid Calculator