When the dots on square dotty paper are joined by straight lines the resulting figures have dots on their perimeter (p) and often internal (i) ones as well.

As such each figure can be described accordingly(p, i). For example, the red square has a (p,i) of (4,0), the grey triangle (3,1), the green triangle (5,0) and the blue shape (6,4).

Below are some examples of figures so described.

How many different figures can be described as (4, 0)?

What do you notice about these (4,0) figures?

Each figure you produce will always enclose an area (A) of the square dotty paper.

The examples in the diagram have areas of 1, 1½, and 6 sq units.

Do you agree?

Draw more figures; tabulate the information about their perimeter points (p), interior points (i) and their areas (A).

Can you find a relationship between all these three variables (p, i and A)?