Find the volume $ V $ of a triangular prism if length $l = 12$ and height $h = 5$.

$V = 200 \sqrt{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 5 $ we have:

$$ 5 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 5 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 10 $$ $$ a = \dfrac{ 10 }{ \sqrt{ 3 } } $$ $$ a = \frac{ 10 \sqrt{ 3}}{ 3 } $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

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

After substituting $ a = \frac{ 10 \sqrt{ 3}}{ 3 } $ and $ l = 12 $ we have:

$$ V =\dfrac{ \sqrt{ 3 } \cdot \frac{ 10 \sqrt{ 3}}{ 3 } ^{ 2 } \cdot 12 }{ 2 } $$$$ V = \dfrac{ \frac{ 100 \sqrt{ 3}}{ 3 } \cdot 12 }{ 2 }$$$$ V = \dfrac{ 400 \sqrt{ 3 } }{ 2 } $$$$ V = 200 \sqrt{ 3 } $$

Triangular Prism Calculator