Congruent Partitions of Polygons

Partition a given polygon $P$ into $n$ mutually congruent pieces so that the area of $P$ not covered by the union of the pieces is as small as possible. A partition which leaves out the least area is an optimal congruent partition for that $n$. If a congruent partition is a perfect cover, leaving no area uncovered, then it is called a perfect congruent partition. Two polygons are congruent if one can be made to coincide with the other by translation, rotation, or reflection (flipping over).