(20 14? Huai 'an) As shown in the figure, connect the midpoints of four sides of a square ABCD with a side length of 1 in turn to obtain quadrilateral a 1 b1c1d1,and then connect quadrilateral A1in tu

(20 14? Huai 'an) As shown in the figure, connect the midpoints of four sides of a square ABCD with a side length of 1 in turn to obtain quadrilateral a 1 b1c1d1,and then connect quadrilateral A1in turn. Connect the midpoints of the four sides of the square ABCD in turn to get the square A1b1c1d1,then the area of the square A 1b 1d 1 is half the area of the square ABCD, that is,/kloc.

Connect the points of the square a1b1c1d1to get the square A2B2C2D2, ABCD the area of the square A2B2C2D2 is the square a1b1d/kloc-0.

Connect squares A2B2C2D2 in turn to get square A3B3C3D3, then the area of square A3B3C3D3 is half that of square A2B2C2D2, that is, 18 of square ABCD, and its perimeter is 24 of square ABCD;

Connect the points of the square A3B3C3D3 in turn to get the square A44B 4C4D4, then the area of the square A44B 4CD4 is half of the area of the square A3B3C3D3, that is, 1 16 of the square ABCD, and its perimeter is14 of the square ABCD;

…

The circumference of that nth square is 12n,

And so on: the circumference of the square A8B8C8D8 is the original 1 16,

The side length of a square ABCD is 1 and the circumference is 4.

∴ The perimeter of the quadrilateral A8B8C8D8 obtained by this method is 14,

So the answer is: 14.