Find the base area $ B $ of a pyramid if height $h = 6$ and slant height $s = 12$.
Answer
$B = 432$
Explanation
STEP 1: find side $ a $
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 6 $ and $ s = 12 $ we have:
$$ 6^2 + \frac{ a^2 }{ 4 } = 12^2 $$ $$ \frac{ a^2 }{ 4 } = 12^2 - 6^2 $$ $$ \frac{ a^2 }{ 4 } = 144 - 36 $$ $$ a^2 = 108 \cdot 4 $$ $$ a^2 = 432 $$ $$ a = \sqrt{ 432 } $$$$ a = 12 \sqrt{ 3 } $$STEP 2: find base area $ B $
To find base area $ B $ use formula:
$$ B = a^2 $$After substituting $ a = 12 \sqrt{ 3 } $ we have:
$$ B = \left(12 \sqrt{ 3 }\right)^2 $$ $$ B = 432 $$This page was created using
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