[Night Stalker]

Actually the triangle bit is a red herring. All three triangles are similar (angles equal, sides proportional), and the total area of the reconfigured large triangle is the same in each case.

The "hole" is created by the differeces in area of the two rectangles that make the difference in the large triangle when the two small triangles are lined up.

With the small triangle on top, the resulting rectangle is 3x5, which has an area of 15.

With the med triangle on top, the resulting rectangle is 2x8, which has an area of 16.

So, when using discreate parts as shown in the picture, there is not enough material to complete the triange in the second configuration, even though the total area is the same for each large triangle.