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question

Solution 1: Median method

Since it is the midpoint, you can use it. If it doesn't work horizontally, use it vertically and expand it to make an auxiliary line.
E is the midpoint S(AED) = 1/4 S(ABCD) = 6
Make an auxiliary extension line in the figure. Since E is the midpoint, S (MEB) = S (AED) = 6
Similarly, E is also the midpoint of MD, so S(MEF) = S(EDF) = 6+4 = 10

Solution 2

Because it is a fill-in-the-blank question, and the length and width of the parallelogram are not restricted, the change in length and width only affects the position of F.
Then make two simplifications to this problem:

1. Simplify a parallelogram into a rectangle
2. Subtract a special value from the length and width of the rectangle to form an area of ​​24, and take AB=4
   Then the lengths of the individual line segments can be calculated, and further the area equals the rectangle minus the perimeter:
   
   During the calculation process, assume that the length and width are 4 and 6.
   We get: AE = 2, S (AED) = 6,
   EB=2, ∵S(EBF)=4, so BF=4, so FC=2 (it can be seen that F is the point of three equal divisions)
   DC=4, FC=2, so S(DFC)=4
   So S(EDF) = S(ABCD) - three triangles = 24 - 6 - 4 - 4 = 10