How to Construct a Hexagon with a Compass and Straightedge

This article provides illustrations and instructions to help students construct a hexagon using a compass and straight edge using a range of methods.

How to draw a hexagon when given a circle (compass method)

You can use this method when you know the distance “across the corners,” (AC). The AC dimension is the same as the diameter, allowing you to draw the circle.

• Draw the circle using the given radius
• Use the compass to step the radius around the circle to find the six points (the radius is equal to the side length)
• Draw in the hexagon

How to draw a hexagon when given a circle (30/60° set square method)

This method is identical to the method above (uses the AC dimension) except that the 30/60° set square is used to draw in the sides.

• Use the given AC dimension to draw the circle (half this to find the radius)
• Use the 30/60° set square to add in 30° and vertical lines (as shown in diagram)
• Draw in the hexagon

How to draw a hexagon given distance across the flats (AF)

• lightly rule two vertical parallel lines, representing the distance across the flats
• Draw a vertical centre line (long dash, short dash)
• Use the 30/60° set square to add in bottom sides of hexagon
• This tells you the length of the sides
• Use the side length to add in the vertical sides and complete the hexagon

How to draw a hexagon when given one side

• Use the side to construct an equilateral triangle (this finds the centre of the circle)
• Scribe a circle from the top of the triangle (radius = length of side)
• Use the compass to step the radius around the edge of the circle to find the points