Tiling with rectangles
{{Short description | Rectangular tilings using various shapes of rectangles}}
A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of {{math|1 × 2}} side
ratio. The tilings with straight polyominoes of shapes such as {{math|1 × 3}}, {{math|1 × 4}} and
tilings with polyominoes of shapes such as {{math|2 × 3}} fall also into this category.
Congruent rectangles
Tilings with non-congruent rectangles
The smallest square that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 11 × 11 square, and the tiling uses five rectangles.{{cite journal|last1=Madachy|first1=Joseph S.|title=Solutions to Problems and Conjectures |journal=Journal of Recreational Mathematics|date=1998|volume=29|issue=1|page=73|issn=0022-412X}}
The smallest rectangle that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 9 × 13 rectangle, and the tiling uses five rectangles.[https://www.viapu.com/herringbone-pattern-in-interior/ Herringbone Tiles on a Bathroom Wall]