Find the lateral area $ L $ of a pyramid if side $a = 12$ and height $h = 18.2$.
Answer
$L = 459.9242$
Explanation
STEP 1: find slant height $ s $
To find slant height $ s $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ h = 18.2 $ and $ a = 12 $ we have:
$$ 18.2^2 + \frac{ 12^2 }{ 4 }= s^2 $$ $$ 331.24 + \frac{ 144 }{ 4 }= s^2 $$ $$ 331.24 + 36 = s^2 $$ $$ s^2 = 367.24 $$ $$ s = \sqrt{ 367.24 } $$$$ s = 19.1635 $$STEP 2: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $ a = 12 $ and $ s = 19.1635 $ we have:
$$ L = 24 \cdot 19.1635 $$$$ L = 459.9242 $$This page was created using
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