STEP 1: find length $ l $

To find length $ l $ use formula:

$$ AL = 3 \cdot a \cdot l $$

After substituting $AL = \dfrac{\sqrt{ 3 }}{ 2 }\, \text{cm}$ and $a = 1\, \text{cm}$ we have:

$$ \frac{\sqrt{ 3 }}{ 2 }\, \text{cm} = 3 \cdot 1\, \text{cm} \cdot l $$$$ \frac{\sqrt{ 3 }}{ 2 }\, \text{cm} = 3\, \text{cm} \cdot l $$$$ l = \dfrac{ \frac{\sqrt{ 3 }}{ 2 }\, \text{cm} }{ 3\, \text{cm} } $$$$ l = \frac{\sqrt{ 3 }}{ 6 } $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

$$ V = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot l }{ 4 } $$

After substituting $a = 1\, \text{cm}$ and $l = \dfrac{\sqrt{ 3 }}{ 6 }\, \text{cm}^0$ we have:

$$ V =\dfrac{ \sqrt{ 3 } \cdot 1\, \text{cm} ^{ 2 } \cdot \frac{\sqrt{ 3 }}{ 6 } }{ 4 } $$$$ V = \dfrac{ \sqrt{ 3 }\, \text{cm}^2 \cdot \frac{\sqrt{ 3 }}{ 6 } }{ 4 }$$$$ V = \dfrac{ \frac{ 1 }{ 2 }\, \text{cm}^2 }{ 4 } $$$$ V = \frac{ 1 }{ 8 }\, \text{cm}^2 $$

Triangular Prism Calculator