To find the area of the base of the box, we can use the formula for the volume of a rectangular prism, which is given by:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
We know the volume is 50 cubic feet and the height is 4 feet. We can rearrange the formula to find the base area:
\[ \text{Base Area} = \frac{\text{Volume}}{\text{Height}} \]
Substituting the known values:
\[ \text{Base Area} = \frac{50 \text{ ft}^3}{4 \text{ ft}} \]
\[ \text{Base Area} = 12.5 \text{ ft}^2 \]
Thus, the area of the base is 12.5 ft².