1. Polygon from a known side
Step 1. Draw a line equal to the length of one side.
Step 2. Bisect the line and draw a perpendicular
Step 3. From one side of the line draw a 600 line
6 sides
Step 4. From the other side of the line draw a 450 line.
4 sides
The 450 line will give you the centre for a circle big enough for a square
600
450
The 600 line will give you the centre for a circle big enough for a hexagon (6 sides)

2. Polygon from a known side
If you bisect the distance between 4 sides and 6 sides you find the centre of a circle for a pentagon (5 sided polygon)
Step 5. Use a compass to bisect the distance. Open the compass to more than the distance and mark an arc from point 4.
6 sides
5 sides
Step 6. Mark an arc from point 6.
4 sides
Step 7. Bisect the distance and mark the centre of the circle for the pentagon.

3. Polygon from a known side
Having set out the centre of the circle, use the following steps to set out the pentagon.
Step 1. Set the compass to the circle radius and draw the circle.
Step 2. Set the compass to the length of the side and step it off around the circle.
6 sides
5 sides
Step 3. Joins up the marks to form the pentagon.
4 sides

4. Polygon from a known side
The same principles apply to the hexagon
Step 1. Set the compass to the circle radius and draw the circle.
Step 2. Set the compass to the length of the side and step it off around the circle.
6 sides
5 sides
Step 3. Joins up the marks to form the hexagon.
4 sides

5. Polygon from a known side
To set the circle centre for other polygons is easy now.
Step 1. Set the compass to the distance between 5 & 6.
9 sides
Step 2. Mark of the distance from 6 along the perpendicular.
8 sides
7 sides
6 sides
5 sides
4 sides

6. Polygon from a known side
Now for a heptagon (7 Sides)
Step 1. Set the compass to the circle radius and draw the circle.
9 sides
Step 2. Set the compass to the length of the side and step it off around the circle.
8 sides
7 sides
6 sides
5 sides
4 sides
Step 3. Joins up the marks to form the heptagon.