Idea: Rectangle is a central symmetrical figure, so the diagonal BD has the same area except the two triangles ABD and CBD, and the areas of the two triangles in the second and fourth quadrants are also equal, so the areas of the two small rectangles in the first and third quadrants are also equal, so k 2+2k+1= 4, and it can be concluded that k = 1 or -3, so D is selected.