A4 paper in the UK measures 210mm on the short side and 297mm on the longer side. If we call the short side one unit in length, the long side is √(2). It is actually too long by less than a tenth of a millimeter, but let’s ignore that. So we have paper with sides 1 and √(2).

To setup the puzzle, we must fold the paper a bit. Fold one of the shorter sides over so it is flush with the longer edge. It should form a triangle. Then, take the corner opposite of the corner that has been turned into a point and fold it to touch the side of the larger triangle. Now, there should be two 45 degree triangles that touch on one side. The first triangle is significantly larger than the second.

Now, the puzzle. What is the perimeter of this shape that is made?

I suggest trying to solve it for yourself! When you are done (or if you are just lazy), here is the solution.

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