To find the height of the triangular prism, you can use the formula for the volume of a prism:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
Given that the volume of the prism is \(20 , \text{cm}^3\) and the area of the base triangle is \(5 , \text{cm}^2\), you can plug these values into the formula:
\[ 20 , \text{cm}^3 = 5 , \text{cm}^2 \times \text{Height} \]
Now, solve for the height:
\[ \text{Height} = \frac{20 , \text{cm}^3}{5 , \text{cm}^2} = 4 , \text{cm} \]
So, the height of the triangular prism is \(4 , \text{cm}\).