A multi-piece floor arrangement and assembly forms a floor covering that includes a top, or upper, rug portion and bottom, or lower, mat portion, and pocketed corner areas in each corner of an underside surface of the rug portion into which corresponding corners of the mat portion are insertable. The pocketed corner areas secure the rug portion with the mat portion when both are placed on an underlying surface while enabling a flow of air between the rug portion and the mat portion. The mat portion includes multiple interlocking sections that help to maintain the floor covering in a uniform planar shape and provide an aesthetically-pleasing appearance when placed on an underlying surface. The multi-piece arrangement and assembly does not move relative to that surface, yet does not require either a cumbersome installation or removal process.