Find the lateral area $ LA $ of a triangular prism if length $l = 13$ and height $h = 2$.
Answer
$AL = 52 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ h = 2 $ we have:
$$ 2 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 2 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 4 $$ $$ a = \dfrac{ 4 }{ \sqrt{ 3 } } $$ $$ a = \frac{ 4 \sqrt{ 3}}{ 3 } $$STEP 2: find lateral $ AL $
To find lateral $ AL $ use formula:
$$ AL = 3 \cdot a \cdot l $$After substituting $ a = \frac{ 4 \sqrt{ 3}}{ 3 } $ and $ l = 13 $ we have:
$$ AL = 4 \sqrt{ 3 } \cdot 13 $$$$ AL = 52 \sqrt{ 3 } $$This page was created using
Triangular Prism Calculator