The nine points of this grid are equally spaced horizontally and vertically. The distance between two neighboring points is 1 unit. What is the area, in square units, of the region where the two triangles overlap?

Using coordinates, we can compute the equation of every line in the diagram, then we compute the coordinates of every point. One of the points of intersection is (1/4,3/4). This gives us an area of 3/2.

The nine points of this grid are equally spaced horizontally and vertically. The distance between two neighboring points is 1 unit. What is the area, in square units, of the region where the two triangles overlap?