The 12 Matches

Assuming that a match is a unit of length, it is possible to place 12  matches on a plane in various ways to form polygons with integral areas. The illustration shows two such polygons: a square with an  area of nine square units, and a cross with an area of five. The problem is this: Use all 12 matches (the entire length of each match must be used) to form in similar fashion the perimeter of a polygon with an area of exactly four square units.

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