Find the volume $ V $ of a triangular prism if length $l = 20$ and height $h = 12$.

$V = 1920 \sqrt{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$

After substituting $ h = 12 $ we have:

$$ 12 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 12 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 24 $$ $$ a = \dfrac{ 24 }{ \sqrt{ 3 } } $$ $$ a = 8 \sqrt{ 3 } $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

$$ V = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot l }{ 2 } $$

After substituting $ a = 8 \sqrt{ 3 } $ and $ l = 20 $ we have:

$$ V =\dfrac{ \sqrt{ 3 } \cdot 8 \sqrt{ 3 } ^{ 2 } \cdot 20 }{ 2 } $$$$ V = \dfrac{ 192 \sqrt{ 3 } \cdot 20 }{ 2 }$$$$ V = \dfrac{ 3840 \sqrt{ 3 } }{ 2 } $$$$ V = 1920 \sqrt{ 3 } $$

Triangular Prism Calculator