Find the volume $ V $ of a triangular prism if length $l = 13$ and height $h = 8$.

$V = \frac{ 1664 \sqrt{ 3}}{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 8 $ we have:

$$ 8 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 8 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 16 $$ $$ a = \dfrac{ 16 }{ \sqrt{ 3 } } $$ $$ a = \frac{ 16 \sqrt{ 3}}{ 3 } $$

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{ 16 \sqrt{ 3}}{ 3 } $ and $ l = 13 $ we have:

$$ V =\dfrac{ \sqrt{ 3 } \cdot \frac{ 16 \sqrt{ 3}}{ 3 } ^{ 2 } \cdot 13 }{ 2 } $$$$ V = \dfrac{ \frac{ 256 \sqrt{ 3}}{ 3 } \cdot 13 }{ 2 }$$$$ V = \dfrac{ \frac{ 3328 \sqrt{ 3}}{ 3 } }{ 2 } $$$$ V = \frac{ 1664 \sqrt{ 3}}{ 3 } $$

Triangular Prism Calculator