Find the lateral area $ L $ of a pyramid if height $h = 30$ and slant height $s = 32$.
Answer
$L = 256 \sqrt{ 31 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 30 $ and $ s = 32 $ we have:
$$ 30^2 + \frac{ a^2 }{ 4 } = 32^2 $$ $$ \frac{ a^2 }{ 4 } = 32^2 - 30^2 $$ $$ \frac{ a^2 }{ 4 } = 1024 - 900 $$ $$ a^2 = 124 \cdot 4 $$ $$ a^2 = 496 $$ $$ a = \sqrt{ 496 } $$$$ a = 4 \sqrt{ 31 } $$STEP 2: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $ a = 4 \sqrt{ 31 } $ and $ s = 32 $ we have:
$$ L = 8 \sqrt{ 31 } \cdot 32 $$$$ L = 256 \sqrt{ 31 } $$This page was created using
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