Shoutbox

Ok on first inspection, it looks like there is a hole magically appearing in the second triangle. But lets work through this problem more closely.

First of all, the pieces used in each triangle are the same. So this leads us to conclude that the surface area of each triangle is the same. Also, on first appearance, the triangles appear to be the same, each with a base of 13 units, and a height of 5 units.

However appearances can be deceptive. The secret to this puzzle is to realise that you are not looking at triangles, but actually quadrilaterals

If you look very closely at the hypotenuse of each triangle (the diagonal line) you will see its not actually straight. There is a very slight bend where the red and green triangles join (I've highlighted this in the attachment).

Due to the way they are arranged, there is a difference in the way the area is distributed. In the first example there is no "hole" as the area is "pushed" to the bottom of the "triangle". In the second instance, there is more area in the top part of the triangle, which means you can cut a hole in the second part. Hopefully my exaggerated diagram will explain this better than words.

In the first picture you see how they don't line up very well. The grey line is for reference to show you how the distribution of the area differs between the 2. In the first the area is below the line. In the second, more of the area is moved above the line which means you can "cut out" some area from below, which produces the "hole".

Mnjul's explaination is also valid, albeit more technical