∴ 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

.