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Constructing a hexagon given one side

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

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 compasses' point on A, and set its width to F. the compasses must remain at this width 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 compasses to O and draw a circle.

This is the hexagon's circumcircle - the circle that passes through all six vertices
4.  Move the compasses on to A and draw an arc across the circle. This is the next vertex of the hexagon.
5.  Move the compasses 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.  

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions