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The real questions in the middle school entrance examination in mathematics
Solution: ∫a 1, F 1, B 1, D 1, C 1, E 1 are the midpoint of each side of △ABC and △DEF respectively.

∴ Regular hexagonal star AFBDCE∽ Regular hexagonal star A1F1B1D1C1E1,and the similarity ratio is 2: 1.

∫ The area of the regular hexagonal star AFBDCE is 1,

∴ The area of regular six-pointed star A/KOOC-0/F/KOOC-0/B/KOOC-0/D/KOOC-0/C/KOOC-0/E/KOOC-0/

1

four

Similarly, the area of the third hexagon is:

1

43

=

1

64

The area of the fourth hexagon is:

1

16

×

1

four

×

1

four

=

1

256

So the answer is:

1

256

.