Box2D mesh collision

First let me quickly say what I'm trying. I am doing a tetris-like game using Box2D, I know that Box2D may not be the best option in this case, but I really need normal physics, because the levels have obstacles, and if you click them, the blocks must rotate.

Here is an image to demonstrate what I mean.

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Case 1: This is how I want it to be.

Case 2: It was one of my ideas, just that the block size of the falling part was a little smaller, so that they fit well into the empty space. As expected, the problem with this was the empty space around the block. Make it look like a field does not belong.

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Update:
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