Martin Garder books have an unending supply of great puzzles, and here is another one from Mathematical Puzzles and Diversions, Chapter 12, puzzle #6.
Given that a match is one unit long, it is possible to arrange 12 matches on a table in various ways to form polygons with areas that are exactly whole numbers. Two such examples are shown below, a square with an area of 9 square units and a cross with an area of 5 square units. The problem is to use all 12 matches to form the perimeter of a polygon with an area of exactly 4 square units.
Please note that there are multiple answers.
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