The magic triangle

A triangle can be made by arranging 4 shapes on a 5 x 13 grid.
By re-arranging the shapes a new triangle can be made.
The  pieces in the lower triangle are exactly the same as those in the upper triangle, but now seem to take up less space so there is one blank square

Where does the white square come from?

[simple_tooltip content=’This trick makes use of an optical illusion. Even though the triangles appear identical the longer edge of the triangle is not a straight line. It bends down lightly in triangle A and bulges upwards slightly in trangle B. Try printing the triangles out and place a ruler against the longer side.’]Hover your mouse here for the solution[/simple_tooltip]

Here is another similar puzzle:

4 similar quadrilateral shapes are arranged into a square.
If each is rotated by 180º they make a similar square but there is a piece missing in the middle.
Where does the extra space come from?

[simple_tooltip content=’The new square is very slightly larger (0.8%) than the original square. For more of the maths on this and the puzzle above goggle Wikipaedia https://en.wikipedia.org/wiki/Missing_square_puzzle ‘]Hover your mouse here for the solution[/simple_tooltip]