Please help!

[Dani052]

There is a 3×3 dot grid. The distance between one point to another is 1. How many different non-congruent polygons can you make on the grid?
Rules:

1. All vertices of the polygon must be on the grid
2. Only non self intersecting polygons
3. Only polygons with non-empty interior (<=> positive area)
4. The area of each polygon is 2
5. At least one side of the polygon is 1.5 or bigger
   
   please help me!

 

[Deleted member 4993]

There is a 3×3 dot grid. The distance between one point to another is 1. How many different non-congruent polygons can you make on the grid?
Rules:

1. All vertices of the polygon must be on the grid
2. Only non self intersecting polygons
3. Only polygons with non-empty interior (<=> positive area)
4. The area of each polygon is 2
5. At least one side of the polygon is 1.5 or bigger
   
   please help me!

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Please share your work/thoughts about this assignment.

 

[Dr.Peterson]

There is a 3×3 dot grid. The distance between one point to another is 1. How many different non-congruent polygons can you make on the grid?
Rules:

1. All vertices of the polygon must be on the grid
2. Only non self intersecting polygons
3. Only polygons with non-empty interior (<=> positive area)
4. The area of each polygon is 2
5. At least one side of the polygon is 1.5 or bigger
   
   please help me!

There is no simple formula for this problem; you just have to think, and think, and think. I would start by trying to draw a few polygons that fit the requirements. As I do that, I expect to learn how it works, and develop ideas for the final answer.

As you tell us your thoughts, we can try to guide them. But you must be in the driver's seat, doing the thinking.