You can have a regular polygon with n sides where the length of each side is 13/n units. For example, a triangle with sides of 4.33... units, or a square with sides of 3.25 units etc.
Or you can have irregular polygons - a triangle with sides of 4,4 and 5 units, etc.
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A paralallogram with a perimeter = 13 units can be made to "lean" over until its area becomes 5 square units.Also:A rectangle with a long side of 5.608495283 and a short side of 0.8915047169 will have a perimeter of 13 units and an area of 5 square units.Also:An isosceles triangle with say 2 legs of 5.5943 and the 3rd leg of 1.8114 will have a perimeter of 13 units and an area of 5 square units.So the answer is that there are many shapes that will satisfy the perimeter and area given.
Perimeter = 6*13 = 78 units
56 apex
13*9 = 117 square units
There are: 13*9 = 117 square units