Find the lateral area $ L $ of a pyramid if side $a = 19.9$ and height $h = 8.2$.
Answer
$L = 513.1615$
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 = 8.2 $ and $ a = 19.9 $ we have:
$$ 8.2^2 + \frac{ 19.9^2 }{ 4 }= s^2 $$ $$ 67.24 + \frac{ 396.01 }{ 4 }= s^2 $$ $$ 67.24 + 99.0025 = s^2 $$ $$ s^2 = 166.2425 $$ $$ s = \sqrt{ 166.2425 } $$$$ s = 12.8935 $$STEP 2: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $ a = 19.9 $ and $ s = 12.8935 $ we have:
$$ L = 39.8 \cdot 12.8935 $$$$ L = 513.1615 $$This page was created using
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