Spoiler for

5. All of the above are possible. Here is how:

1. Pythagorean traingle with sides 3, 4, 5.

2. A triangle formed by three verices of a unit square.

3. Two triagles as above glued along short side.

4. Equilateral triangle with unit area.

1. Pythagorean traingle with sides 3, 4, 5.

2. A triangle formed by three verices of a unit square.

3. Two triagles as above glued along short side.

4. Equilateral triangle with unit area.