An octagon is a polygon with eight sides. In general, when people think of the word "octagon", they think of the "regular octagon" - one that has corners and sides of the same size (like Stop signs). It is easy to create an accurate octagon in many ways, using only simple materials - start with Step 1 below.
Steps
Method 1 of 4: Using a Ruler and Protractor
Step 1. Determine the side length of your octagon
Since the dimensions of the corners of a regular polygon are fixed, the only measurement you need to establish the size of the octagon and that of the side. The larger the side, the larger the octagon itself will be. Decide according to the space you have available to draw.
Step 2. Use a ruler to draw a line of the predetermined length
It will be the first of the eight sides. Draw the line at a point that allows you to accommodate the rest of the polygon.
Step 3. Using a protractor, mark an angle of 135or relative to the line.
Find and mark the angle of 135or also at the other end of the line. Draw a line the same length as the first one, starting at the angle of 135or. This will be the second side of the octagon.
Note that the lines must meet at the end points. Don't start the new line in the middle of the old one, for example
Step 4. Continue making lines with 135 anglesor compared to the previous ones.
Follow this pattern until you have created a complete regular octagon.
Due to the small human errors that accumulate in your drawing, the last side you will draw may not respect the angle of 135or. Usually, if you have drawn carefully, you can simply use the ruler to connect the end of the seventh side with the beginning of the first.
Method 2 of 4: Using a Compass and Ruler
Step 1. Draw a circle and two perpendicular diameters
Compasses are simple tools used to draw perfect circles. The diameter of the circle you drew will be the largest diagonal of the octagon - in other words, the distance from one corner of the octagon to the one directly opposite. A larger circle will therefore give rise to a larger octagon. Use a compass to draw the circle and after doing so, draw two perpendicular diameters that meet in the center of the circle.
Step 2. Draw a slightly larger circle concentric to the first one
Holding the compass in the same place, draw a circle with a slightly larger radius. For example, if the original radius is 5cm, you could add 1.5cm to the radius and draw another circle.
For the rest of the process, hold the compass with this new, wider opening
Step 3. Draw an arc in the center of the circle
Place the center of the compass on one of the intersections between the inner circle and its diameter. Use the tool to draw an arc near the center of the circle. You don't have to draw a full circle - an arc that goes from one point to the other on the circumference will suffice.
Step 4. Repeat on the opposite side
Put the center of the compass at the intersection of the inner circle and its diameter at the point opposite the one you just used and draw another arc in the center of the circle. You should draw an "eye" shape in the center of the circle.
Step 5. Draw two lines that pass from the corners of the eye
Use a ruler to do this. The lines must be long enough to intersect the circle at two points and perpendicular to the diameter they cross.
Step 6. Draw two arcs from the remaining intersection points between the inner circle and its diameters
Now, repeat the previous steps for the "other" diameter that forms the central cross. In other words, put the center of the compass at the intersection point between the second diameter and the circumference and draw arcs in the center of the circle.
When you are done, you should see two "eyes" that intersect
Step 7. Using a ruler, draw lines from the corners of the new eye
As before, you will need to draw two straight lines across the corners of the eye. The lines must be long enough to intersect the circle at two points and perpendicular to the diameter they cross.
When drawing, these lines should form a square with the lines drawn from the other eye
Step 8. Connect the corners of the "square" you just completed to the intersection of the central cross and the inner circle
These points form the corners of a regular octagon. Connect them to complete the octagon.
Step 9. Erase the circle, lines and arcs, leaving only the octagon
Congratulations! You just drew a regular octagon!
Method 3 of 4: Folding the Paper
Step 1. Start with a square piece of paper
Note that almost all types of paper used at work or school are rectangular rather than square. Printer paper for example is usually 21.59cm x 27.94. This means you will need to find a square sheet (thick cardstock has this shape) or cut out one side of the paper to make the sheet square.
If you decide to cut paper, use a ruler to ensure accuracy. For example, if you want to cut an A4 sheet into a square, use a ruler to measure the length of the shorter side on the longer one, then cut it
Step 2. Fold the corners of the square inward
Note that doing so will create an eight-sided shape. These folds will serve as four sides of the octagon, therefore, it is important that they are the right size if you want to make a regular polygon. Use a ruler to measure the folded edges - you'll want the sides to be as close as possible to the space between them.
Note that you shouldn't fold the corners all the way in. If you did, you'd be left with a smaller square. Instead, fold them about halfway from the center
Step 3. Cut with scissors along the folded sides
When you are happy with the size of your octagon, partially unfold the corners of the paper and cut along the folds. You should get an eight-sided shape with sides roughly the same length - a regular octagon.
Method 4 of 4: Create an Irregular Octagon
Step 1. Use eight sides of varying lengths
It is worth mentioning that although almost all people use the word "octagon" to refer to the regular octagon (one with sides and angles of the same size), it is not, in technical terms, the only type of octagon in existence.. Any eight-sided shape is an octagon by definition. So by drawing a shape with eight sides of different lengths, you get an irregular octagon.
Step 2. Use different sized angles
As with the length of the sides, octagons don't have to have all angles of 135or. If your shape has eight sides, whatever the angles are, it can be called an octagon.
The exception to this rule are angles which measure exactly 180or. In general, the two lines that form a flat corner can be considered a single side in a polygon.
Step 3. Use intersecting sides
It is worth noting that there are special types of polygons, called "star polygons" which have lines that cross each other. For example, a classic five-pointed star is drawn from five lines that intersect at multiple points. In the same way it is possible to make an eight-pointed star from eight lines of equal length. It is also possible to make figures with eight sides that intersect without creating a symmetrical and orderly star. These shapes can often be considered "special" octagons.
Advice
- You have to be precise if you want to draw a perfectly regular octagon.
- It's easier to fold the paper, or another material, and build the octagon from a square to get smoother sides.
