After doing this	Your work should look like this
We start with a line segment AF. This will become one side of the hexagon. Because we are constructing a regular hexagon, the other five sides will have this length also.
1.  Set the compass point on A, and set its width to F. The compass will remain at this setting for the remainder of the construction.
2.  From points A and F, draw two arcs so that they intersect. Mark this as point O. This is the center of the hexagon's circumcircle.
3.  Move the compass to O and draw a circle. This is the hexagon's circumcircle - the circle that passes through all six vertices
4.  Move the compass on to A and draw an arc across the circle. This is the next vertex of the hexagon.
5.  Move the compass to this arc and draw an arc across the circle to create the next vertex.
6.  Continue in this way until you have all six vertices. (Four new ones plus the points A and F you started with.)
7.   Draw a line between each successive pairs of vertices.
8.   Done. These lines form a regular hexagon where each side is equal in length to AF.

Explanation of method

This construction is very similar to Constructing a hexagon inscribed in a circle, except we are not given the circle, but one of the sides instead. Steps 1-3 are there to draw this circle, and from then on the constructions are the same.

The center of the circle is found using the fact that the radius of a regular hexagon (distance from the center to a vertex) is equal to the length of each side. See Definition of a Hexagon.

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Parallel line through a point
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object