The puzzle rearrangement of triangle is as follows:Now how is that possible?
Solution to the so called Triangle Rearrangement or Disappearing Tile Puzzle (click here) :
It just looks as if the both the triangles are of same size, but actually they are not. There is only a slight difference in both the triangles which you tend to miss out even when you try them on paper cut outs, thinking that you were not perfect with cutting!!
The main difference comes in the inclined line of the triangle, i.e. the slope of the line.
The small change is slope is from 0.4 to 0.375. This small change is enough to accommodate the area of 1x1 area in the triangle.