The total area occupied is the same on both the top and bottom figure. If you look carefully the two triangular pieces have slightly different slopes. So it's just an optical illusion of some sort. Hope it helps.

This is a "math" puzzle. You can also take the shapes and form 1. square 2. rectangle 3. rectanle border Thare are also various other shapes you can make with these pieces. It becomes especially fun when you want to do the math that goes along with the puzzle.

Look at the slopes of the two triangles. They are different. The green triangle is 2/5, the red is 3/8. This causes the hypotenuse of the top triangle to bow inward a bit. The bottom triangle bows outward a bit, which is where the seemingly extra area goes.

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its not an optical illusion and its really quite simple to understand. if you have a box filled with some things arranged in a particular way, if you take them out and arrange it differently, they might not fit as neatly. Thats what is happening.

What's happening is an optical illusion that makes you think the hypotenuse is straight, but actually the hypotenuses of the small triangles do not align, they have different angles. I made a quick drawing to better answear your question. In my drawing I exaggerated that difference so you can better see what I'm talking about. The first "triangle" is actually a concave quadrilateral, and the second triangle is convex quadrilateral. In the third I overlaid both and painted blue the difference between both areas. This blue difference is precisely the area of that missing square. In simpler words, what's happening is that in your first triangle, the square that disappeared in the second one is stretched along the fake hypotenuse. Hope you get it...