Answer
The answer is 2.
Solution
Consider the following diagram.
Notice that lines AB and CD are both at 45-degree angles. Thus, they are parallel.
Recall that the area of a triangle is (1/2) × base × height. So, it doesn't make any difference how big the blue square is. The height of triangle ABC will always be the same. The area is the same as triangle ABD, because D has the same height as any C.
Simple geometry shows AB = sqrt(2) and BD = 2*sqrt(2). Thus, the area of ABC = ABD = (1/2) * sqrt(2) * (2*sqrt(2)) = 2.