Calculate Parallelogram Area: 90° Perpendicular Height and 40-Unit Side

To solve this problem, we analyze the given data:

• The parallelogram $ABCD$ is defined, where side $AD = 40$.
• A perpendicular segment $FE$ of length 90 is given, with the angle $\angle AFE = 90^\circ$.

Commonly, the area of a parallelogram is calculated using the formula: Area = Base $\times$ Height. However, the problem lacks definition of what constitutes the height directly applicable to either base $AD$ or any other base in the parallelogram's configuration.

The segment $FE$ is noted, but it is unclear whether it functions as a height properly aligned perpendicular to a base of relevancy within the parallelogram $ABCD$, given this configuration.

Therefore, without additional context establishing the height using these segments and the position of $E$ and $F$, the problem cannot calculate a definitive area for the parallelogram.

Based on problem statement challenges and insufficient guidelines explicitly establishing perpendicular relationships that function for the area calculations, the problem is designated unresolved for a clear-area determination.

Therefore, the correct conclusion in such an indeterminate case is: Cannot be solved.