Find the lateral area $ L $ of a pyramid if side $a = 8$ and lateral edge $e = 8$.
Answer
$L = 64 \sqrt{ 3 }$
Explanation
STEP 1: find slant height $ s $
To find slant height $ s $ use Pythagorean Theorem:
$$ s^2 + \frac{ a^2 }{ 4 } = e^2 $$After substituting $ a = 8 $ and $ e = 8 $ we have:
$$ s ^ {\,2} + \frac{ 8^2 }{ 4 } = 8^2 $$ $$ s ^ {\,2} + \frac{ 64 }{ 4 } = 8^2 $$ $$ s ^ {\,2} + 16 = 8^2 $$ $$ s ^ {\,2} = 64 - 16 $$ $$ s ^ {\,2} = 48 $$ $$ s = \sqrt{ 48 } $$$$ s = 4 \sqrt{ 3 } $$STEP 2: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $ a = 8 $ and $ s = 4 \sqrt{ 3 } $ we have:
$$ L = 16 \cdot 4 \sqrt{ 3 } $$$$ L = 64 \sqrt{ 3 } $$This page was created using
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