can anyone explain what's happening here ?

I loaded it into photoshop, cut each piece on the top drawing and placed them over their new locations on the bottom one, they all fit, but there's still that empty square.


very very confused...
 
I'm confused - if you calculate the area of the entire triangle, you get an area of 32.5 square units. But, if you calculate the area of each piece - large triangle, small triangle, and rectangular section, you get 12 + 5 + 15 square units which only adds up to 32.
 
I'm confused - if you calculate the area of the entire triangle, you get an area of 32.5 square units. But, if you calculate the area of each piece - large triangle, small triangle, and rectangular section, you get 12 + 5 + 15 square units which only adds up to 32.


I don't understand. I can completely overlap the top triangle over the bottom one. Also, if you rotate the top triangle and place it on the bottom, it makes a perfect rectangle.
 
It works because the two smaller triangles have different shapes, which means the hypotenuse of the big triangle isn't a straight line.

In the first one, the hypotenuse is pointed inwards, and the second one, it's pointed outwards, which is where the space from the empty box goes.
 
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