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There are exactly three possible ways to make a quadrilateral by combining two pentominoes.

Pentominoes are made of squares connected along their edges, so they have only right angles. This means the only quadrilaterals we can make from them will be rectangles. By definition, each pentomino has an area of 5 , so combining two of them will give us a rectangle made of 10 squares. This must be the 10x1 rectangle or the 5x2, because these are the only factors of 10.

All possibilities are listed below:

10x1 rectangle:

  • Two 5x1 pentominoes connected end-to-end.
5x2 rectangle:
  • Two "L pentominoes" laying on each other.
  • Two "P pentominoes" poking into each other.
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Q: How do you make a quadrilateral with two pentomino pieces?
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