How to Construct Regular Polygons Using a Circle

Constructing accurate polygons is very significant in geometry and easy to do. If you have ever wondered about how to construct regular polygons from a circle, you’re reading the right article.

EditSteps

EditUsing A Protractor

1. Draw a circle to the desired amount of circle size. Use your compass to do this.
   
   
   
   
   
   
   
   
   
   • There should be a mid-point. If there is, lightly draw a straight line using a ruler across the circle by using the mid-point.
     
     
     
     
   
   
   
   


2. Divide the circle. Since a circle has 360 degrees, divide 360 degrees to the amount of vertices you have. For instance, use a dodecagon. This shape has 12 vertices, so 360 degrees divided by 12 comes out to be 30 degrees.


3. Mark a point for every divided amount (the dodecagon’s divided amount equals to 30 degrees as shown in the example before) with a protractor and pencil. Make sure you start at the line you have drawn.
   
   
   
   


4. Join the lines together for every mark you did (there should be 12 marks for a dodecagon because it has 12 vertices). Don’t overlap the lines.
   
   
   
   
   
   
   • If your points are outside of the circle, then simply mark another point onto the circle’s line for each point that is on the outside. Then, you can join them.
   
   
   
   


5. Check to see if the sides are the same in length and width. If they are, you can rub out the outside circle.


6. Finished.
   
   
   
   

EditUsing A Compass

1. Draw a circle to the desired amount of circle size. Use your compass to do so.
   
   
   
   
   
   
   


2. Start from any point on the circle and mark an arc or line. Don't change the radius of your compass.
   
   
   
   
   
   
   


3. Mark another arc or line on the circle's line. Continue the process until the arc or line touches the first point. This will make a hexagon (6 arcs/lines) and only works for a dodecagon, triangle and a hexagon.
   
   
   
   
   
   
   
   
   
   • Make sure your compass doesn't move!
   
   
   • To make a dodecagon, measure the radius of the circle and half it on your compass and mark lines. It should mark 12 lines.
   
   
   • To make a triangle, measure the radius of the circle and double it on your compass and mark lines. It should mark 3 lines.
   
   
   
   


4. Join the lines/arcs accurately using a ruler.
   
   
   
   
   
   
   
   
   
   • Check to see if the sides are identical in length and width.
   
   
   • If they are, then you're finished. Rub the guidelines.
     
     
     
     
     
     
     
   
   
   
   

EditTips

• If you want, you could draw the circle and mark the points lightly.

EditWarnings

• This works for a heptagon or with a divided angle amount with decimals, but it may not be that accurate. Guess the decimal position on the protractor.

EditThings You’ll Need

• Protractor


• Paper


• Pencil


• Eraser


• Compass

EditRelated wikiHows

• How to Draw a Hexagon


• How to Draw a Polygon

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