Find the lateral area $ L $ of a pyramid if side $a = 13$ and height $h = 17$.
Answer
$L = 65 \sqrt{ 53 }$
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 = 17 $ and $ a = 13 $ we have:
$$ 17^2 + \frac{ 13^2 }{ 4 }= s^2 $$ $$ 289 + \frac{ 169 }{ 4 }= s^2 $$ $$ 289 + \frac{ 169 }{ 4 } = s^2 $$ $$ s^2 = \frac{ 1325 }{ 4 } $$ $$ s = \sqrt{ \frac{ 1325 }{ 4 } } $$$$ s = \frac{ 5 \sqrt{ 53}}{ 2 } $$STEP 2: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $ a = 13 $ and $ s = \frac{ 5 \sqrt{ 53}}{ 2 } $ we have:
$$ L = 26 \cdot \frac{ 5 \sqrt{ 53}}{ 2 } $$$$ L = 65 \sqrt{ 53 } $$This page was created using
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