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If you draw a diagonal through the center of the square, you get two halves. When you connect one vertex to the midpoint of the opposite sides, you have cut the diagonal in half. So each of the right triangles is one fourth of the square. The smaller triangle is one eighth of the square. If you were to put two of the small triangles together to create a square, it would take up one-fourth of the larger square; half of one fourth is one eighth. The larger triangle in the center is three eighths (1/4 + 1/4 + 1/8=5/8. so the remaining piece is 3/8). The bottom figure is simply four sets of the top figure reflected across center lines of symmetry. The four triangles combine to create a parallelogram. The proportion of the piece does not change; it is still one fourth of the square.