The correct answers to this question are ② and ④, and the other answers are incorrect. S 1 and S3 are two triangles with equal bases, and the sum of their heights is exactly equal to the length of the other side of the rectangle, so the sum of their areas is equal to half the area of the rectangle. Similarly, the sum of S2 and S4 is equal to half the area of this rectangle, so ② is the correct answer; Using the similarity, we can know that ④ is also correct. As for why ① and ③ are wrong, it is usually enough to give a counterexample. For ①, it holds only when the point P is on the diagonal BD of the rectangle; For ③, as long as the point P is located on the line segment of the straight line parallel to AD in the rectangle, and the distance from AD is equal to one third of the length of AB, S3=2S 1, but the relationship between S2 and S4 at this time varies with the position of the point P. 。