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Using A ProtractorUsing A Compass, Ruler and Calculator

Edited by Mike, Deniseke, Adelaide, Krystle and 6 others

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

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Method 1 of 2: Using A Protractor

  1. 1
    Draw a straight line using the protractor. This will be the center line of the circle (dividing it into hemispheres).
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  2. 2
    Align the protractor with both 0° and 180°on the center line, then mark the center point.
  3. 3
    Trace the semicircle along the protractor from 0 ° to 180°.
  4. 4
    Put the protractor on the other side of the center line, again with the both the 0°and 180° protractor markings on the center line.
  5. Step_1 1.png
    5
    Complete the circle by tracing along the protractor.
  6. 6
    Calculate the angle between adjacent vertices, α. Since a circle has 360°, divide 360° by n, the number of vertices (or sides) to get α.
    • α=360°/n
    • α is the measured angle between lines drawn from the center of the circle to adjacent vertices.
    • For a dodecagon, n=12. A dodecagon has 12 sides and 12 vertices, so 360° divided by 12 comes out to be 30° and α=30°.
  7. Step_3.png
    7
    Mark a point for each of the successive angles. Using the protractor, mark all the multiples of the angle α calculated above.
  8. Step_5.png
    8
    Join the points marked on the circle with a line segment. For a dodecagon there should be 12 marks and 12 sides because it has 12 vertices. Don’t overlap the line segments.
    • If your points are outside of the circle, then simply mark another point along the radial line from the center onto the circle for each point and then join them.
  9. 9
    Check to see that the sides are the same length. If they are, you can rub out the circumscribed circle.
  10. Step_7.png
    10
    Finished.

Method 2 of 2: Using A Compass, Ruler and Calculator

  1. Draw a Circle Step 6.jpg
    1
    Draw a circle of the desired radius, r. Set your compass to the radius, r, and draw a circle.
  2. 2
    Calculate the length, ℓ, of each side of the regular polygon of n sides.
    • ℓ=2*r*sin(180/n)
    • 180/n is in degrees, so make sure your calculator is set for degrees, not radians.
  3. 3
    Set your compass to this length, ℓ. Be ultra-accurate and triple check the measurement to ensure that it is as accurate as possible.
  4. Draw a Hexagon Step 3 Version 2.jpg
    4
    Start from any point on the circle and mark an arc or line. Don't change the radius of your compass.
  5. Center
    5
    Mark another arc or line on the circle. Continue the process until the arc or line touches the first point.
    • Make sure your compass doesn't move!
  6. Draw a Hexagon Step 7 Version 2.jpg
    6
    Join the lines/arcs accurately using a ruler.
    • Check to see that the sides are identical in length.
    • If they are, then you're finished. Rub out the construction guide lines.
      Draw a Hexagon Step 8 Version 2.jpg
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Tips

  • For the ultimate construction, do all of the marks in fine line black pen, then paperclip a piece of tracing paper to your ink drawing and do the tracing carefully in pen or pencil.
  • If you use a mechanical pencil, rotate the pencil slightly as you draw. This will produce a strong, consistent line. Otherwise, the lead wears and the line increases in boldness/width.
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Things You’ll Need

Method One

  • Protractor
  • Calculator (optional, but maybe necessary depending on the number of sides)
  • Paper
  • Tracing paper (optional)
  • Pencil
  • Pen - black, fine point (optional)
  • Eraser

Method Two

  • Compass
  • Ruler
  • Calculator
  • Paper
  • Tracing paper (optional)
  • Pencil
  • Pen - black, fine point (optional)
  • Eraser

Related wikiHows

How to
Draw a Polygon

How to
Draw a Hexagon


Article Info

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Categories: Featured Articles | Geometry

Recent edits by: Alabaster, Abhishek, Uraretard11

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