∴ 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
.