(1) According to the theorem that the center line of a triangle is parallel to the base, it is proved that A1b1c1d1is a parallelogram.

Due to the AC vertical BD, it can be proved that

(2) According to the fact that the diagonals of the rectangle are equal, the bit line in the triangle is equal to half of the bottom, and A2B2C2D2 is a diamond.

The two diagonal lines of the diamond are exactly equal to the length and width of the rectangle.

According to the area formula of rectangle = length × width

And the area formula of diamond = 1/2x diagonal x diagonal.

The ratio of the two areas is 2/ 1.

(3) The quadrilateral inside the diamond is a rectangle, which is proved as (1).

The length of the small rectangle is equal to half of the long diagonal of the diamond, and the width is equal to half of the short diagonal.

As we all know, the area of a small rectangle is half that of a diamond.

So there must be a rule.

S2= 1/2S 1

S3=( 1/2)^2S 1

...

sa=( 1/2)^(a- 1)s 1

S 1= 1/2*6*8=24

So the required area = 24 * [1/2 (A- 1)].