Welcome to


Grandpa Pencil
learns the secret of
Drawing Polygons


The secret code

Regular polygons consist of a range of figures whose sides are equal and fit exactly into a circle.

Equilateral triangles and squares are regular polygons as are pentagons, hexagons and nonagons, among others and are extremely difficult to draw unless you know the secret code.

If you draw radii, from the centre of a circle, to adjacent corners of your polygon, at the outer edges of the circle, they will form angles, at the centre, of 360 degrees divided by the number of sides.

If you draw a square, therefore, the four angles at the centre of the circle will each be 90 degrees (360 divided by 4 equals 90).

How to draw one

Obviously you will need some method of drawing a perfect circle.
This may be a large or little compass or, for larger circles, a nail, a piece of string and a pencil or piece of chalk.

Scribe a circle ensuring that you have its centre marked then draw a line from the centre to the outer edge of the circle.

Having decided which polygon you need to draw, find the angle that your next radius must be against your first from the table below and, with a protractor and straight edge, draw that radius to the edge of the circle.

Continue until all of the radii are drawn then simply join up those lines where they meet the edge of the circle. Now that's difficult isn't it.


The table, below, gives the angles for some of the polygons.

Name of
the Polygon
Number
of Sides
Angle at Centre
(degrees)

Equilateral Triangle

3
120

Square

4
90

Pentagon

5
72

Hexagon

6
60

Heptagon

7
*51 3/7

Octagon

8
45

Nonagon

9
40

Decagon

10
36

* fifty-one and three sevenths degrees


     

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