A rectangle is placed inside an isoceles right triangle in such a way that the two vertices of the rectangle lie on the hypotenuse, and the other two vertices lie on the legs.

The area of the triangle is 2 square units, and the area of the rectangle is one quarter of that.

In the diagram thus created, find the area of the triangle which does not touch the hypotenuse of the larger, isoceles triangle.
 

Note: For clarity, this problem has been reworded to say 'hypotenuse of the larger, isoceles triangle', rather than 'base of the larger, isoceles triangle'.