Find the base area $ B $ of a pyramid if height $h = 8$ and slant height $s = 10$.
Answer
$B = 144$
Explanation
STEP 1: find side $ a $
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 8 $ and $ s = 10 $ we have:
$$ 8^2 + \frac{ a^2 }{ 4 } = 10^2 $$ $$ \frac{ a^2 }{ 4 } = 10^2 - 8^2 $$ $$ \frac{ a^2 }{ 4 } = 100 - 64 $$ $$ a^2 = 36 \cdot 4 $$ $$ a^2 = 144 $$ $$ a = \sqrt{ 144 } $$$$ a = 12 $$STEP 2: find base area $ B $
To find base area $ B $ use formula:
$$ B = a^2 $$After substituting $ a = 12 $ we have:
$$ B = 12^2 $$ $$ B = 144 $$This page was created using
Pyramid Calculator