Find the lateral area $ L $ of a pyramid if side $a = 6$ and height $h = 14$.
Answer
$L = 12 \sqrt{ 205 }$
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 = 14 $ and $ a = 6 $ we have:
$$ 14^2 + \frac{ 6^2 }{ 4 }= s^2 $$ $$ 196 + \frac{ 36 }{ 4 }= s^2 $$ $$ 196 + 9 = s^2 $$ $$ s^2 = 205 $$ $$ s = \sqrt{ 205 } $$STEP 2: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $ a = 6 $ and $ s = \sqrt{ 205 } $ we have:
$$ L = 12 \cdot \sqrt{ 205 } $$$$ L = 12 \sqrt{ 205 } $$This page was created using
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