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Well, if you can figure out how this works, you're smarter than me.


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That is quite perplexing to have part of the same surface area free just by rearranging the shapes. Obviously it shouldn't be possible. I'm stumped too.
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Take a careful look at the upper figure: it's not a perfect triangle (the part where the blue starts slopes up more steeply than the rest). Same goes for the lower figure really. So, by smuggling tiny little bits here and there, extra surface area can be created to allow for a free black square.

The arrangement of the black lines isn't similar across the two figures either.

Just to illustrate:





I've highlighted two obvious differences.

See?
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Ah! So the top edge of the total triangle isn't straight! Very sneaky!
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I should send this one to the Darwin Awards.











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