Polygon made up of 12 unit sticks with an area limit

Question

A polygon is made up of 12 unit sticks and its area is 3 units^2. Find as many such polygons as possible. Note that a side of the polygon could be made up of more than 1 stick but a stick could not be cut/bent.

Answer 1

Consider unit shapes such as
1. 3,4,5 triangle
2. Squares
3. Equilateral triangles
4. diamonds whose area + equilateral area = 1
5. 6 pointed stars

From 1, you'll need to remove 3 squares, easily done. For the 2 trominos, they both use 8 matches. Substitute 2 in and 2 out equi-triangles For the 5 tetrominos, you'll need to skew a square into a diamond, and then subtract a triangle.

There are more shapes, but they get more irregular.