Find the height $ h $ of a triangular prism if length $l = 12$ and lateral $AL = 360$.
Answer
$h = 5 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ AL = 3 \cdot a \cdot l $$After substituting $ AL = 360 $ and $ l = 12 $ we have:
$$ 360 = 3 \cdot a \cdot 12 $$$$ 360 = 36 \cdot a $$$$ a = \dfrac{ 360}{ 36 } $$$$ a = 10 $$STEP 2: find height $ h $
To find height $ h $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ a = 10 $ we have:
$$ h = \dfrac{ \sqrt{ 3 } \cdot 10 }{ 2 } $$$$ h = \dfrac{ 10 \sqrt{ 3 } }{ 2 } $$ $$ h = 5 \sqrt{ 3 } $$This page was created using
Triangular Prism Calculator