38264

The least amount of line needed is one line dividing the central 2 triangles of the square in half.

I knew that the diagram had 18 triangles which is a number not divisible by 4. So I divided 2 triangles in half to have a total of 20 triangles which is a number divisible by 4. At first I drew the smaller triangles at the side of the square but this did not work. Then I divided all of the triangles in half using 9 lines giving me 36 triangles. I successfully divided the diagram into equally sized quarters of the same shape, but this did not give me the smallest amount of line. Once more I split 2 triangles in half but this time the halved triangle was in the middle.