Find the lateral area $ L $ of a pyramid if side $a = 6$ and height $h = 4$.
Answer
$L = 60$
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 = 4 $ and $ a = 6 $ we have:
$$ 4^2 + \frac{ 6^2 }{ 4 }= s^2 $$ $$ 16 + \frac{ 36 }{ 4 }= s^2 $$ $$ 16 + 9 = s^2 $$ $$ s^2 = 25 $$ $$ s = \sqrt{ 25 } $$$$ s = 5 $$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 = 5 $ we have:
$$ L = 12 \cdot 5 $$$$ L = 60 $$This page was created using
Pyramid Calculator