Polygons

Drawing regular Polygons is now most easily accomplished using modern drafting aids and Computer Aided Design tools. But there are occasions when it is useful to have an understanding of some basic constructions using just rule and compasses (or pegs and pieces of string). Examples might include large scale work for stage sets or carnival floats, or on-site work for buildings, playgrounds, sports fields and gardens.

The following examples are limited to constructions of regular polygons. Irregular polygon construction may be achieved using a process of triangulation, vectors, coordinates or plotting points on a matrix for example. Some other polygons (e.g. Cyclic Quadlitateral) have particular properties which can be helpful to know when constructing them.

See also the YouTube video All the possible polygons!. This shows how all regular polygons can be constructed using classical geometry techniques

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Note: Some constructions on the YouTube video may be different to those described below - there are several methods of construction possible for most regular polygons.

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Equilateral Triangle	Draw a line of length equal to the length of side required. From each end of the line, strike arcs using the line length as radius. Where they intersect will provide the top apex of the required triangle.
Square	Draw a line of length equal to the length of side required. From one end of the line construct a perpendicular - (see Basic Constructions). Set the line length as a radius and strike an arc along the perendicular to find the second side of the square. Keep the same radius and strike arcs from the ends of the two adjacent sides as shown Joining to where the two arcs intersect provides the remaining two sides.
Pentagon	Draw a line of length equal to the length of side required and construct its perpendicular bisector - (see Basic Constructions). From one end of the base line construct 450 and 600 angles. Where these to angles cross the vertical centre line would mark the centres of circumscribing circles for squares and hexagons respectively Bisect between these two centres and draw a circle which circumscribes the pentagon. Set radius to the length of side
Hexagon	###
Octagon	###