How can this be done Below The four parts are moved around. The partitions are exactly the same as those above?

The reason for the extra space comes from the fact that while the hypotenuses of the red and green triangles appear to form one continuous line, they are actually slightly different. Since the slopes of the two triangles are not exactly the same (3/8 or .375 vs 2/5 or .4), the top triangle bows slightly inward while the bottom triangle bows slightly outward. The "hole" comes from this slight difference. The area under the triangles in the second picture is 16 squares (8 x 2) and the area under the triangles in the first picture is 15 (5 x 3).