The first thing to do is divide the figure into a number of sections which is a multiple of four. The easiest way to do this is to split it up into smaller triangles:
Note that there are now 12 sections, which divides into sections of 3. Three triangles forms a square and a smaller triangle. We know, as a result, that a square must go here (another way to do this is that the triangle in the corner must be part of a shape of three parts):
From this, it becomes clear where the rest of the divisions lie. The remaining triangle, as part of the triangular section, must be part of a set of three, so as a result, we know that it is as follows:
The rest of the divisions are simple:
And, as a side note, for future reference, LiveGeometry is a wonderful little tool.