That wouldn't work if the large shape were a triangle. It's not, but the optical illusion caused by the near-indetectible change in slope of the lines of the smaller triangles makes you think you can use basic triangle geometry to try to solve the puzzle.
I started to see something was wrong when I added up the areas of the smaller shapes and came up with 32 units, and when I tried calculating the area of the large "triangle", I came up with 32.5 units.
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