Find the lateral area $ LA $ of a triangular prism if length $l = 26$ and height $h = 9$.
Answer
$AL = 468 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ h = 9 $ we have:
$$ 9 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 9 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 18 $$ $$ a = \dfrac{ 18 }{ \sqrt{ 3 } } $$ $$ a = 6 \sqrt{ 3 } $$STEP 2: find lateral $ AL $
To find lateral $ AL $ use formula:
$$ AL = 3 \cdot a \cdot l $$After substituting $ a = 6 \sqrt{ 3 } $ and $ l = 26 $ we have:
$$ AL = 18 \sqrt{ 3 } \cdot 26 $$$$ AL = 468 \sqrt{ 3 } $$This page was created using
Triangular Prism Calculator