Connecting the midpoint of four sides edge to edge, we can see that the big square is divided into four equal small squares, and the square connected by the midpoint is divided into four isosceles right triangles, each triangle is half of the small square, so this square is half the area of the big square, that is, 10000/2=5000 square meters.
Similarly, the middle connecting the four sides of this square is equal to half the area of the previous square, that is, 5000/2=2500 square meters.
So the area of this square lawn =100 *100 ÷ 2 ÷ 2 = 2500 corn.