The volume \( V \) of a right rectangular prism can be calculated using the formula:
\[ V = \text{Base Area} \times \text{Height} \]
Given that the volume \( V \) is 50 cubic units and the height is 2 units, we can rearrange the formula to find the base area \( A \):
\[ A = \frac{V}{\text{Height}} = \frac{50}{2} \]
Calculating this gives:
\[ A = \frac{50}{2} = 25 \text{ square units} \]
Thus, the area of the base is \( \boxed{25} \) square units.