To find the height of the triangular prism, we can use the formula for the volume of a prism:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
Given:
- Volume = \(20 , \text{cm}^3\)
- Base Area = \(5 , \text{cm}^2\)
We can rearrange the formula to solve for the height:
\[ \text{Height} = \frac{\text{Volume}}{\text{Base Area}} \]
Now, plug in the values:
\[ \text{Height} = \frac{20 , \text{cm}^3}{5 , \text{cm}^2} = 4 , \text{cm} \]
Therefore, the height of the prism is \(4 , \text{cm}\).