3 Ways to Draw a Polygon

Want to learn how to draw a polygon? Polygons are closed figures formed by straight line segments. There are different types of polygons, but they all have two characteristics in common: an equal number of sides and vertices.

Steps

Step 1. Decide which type of polygon to draw

Polygons are classified according to their total number of sides. For example, a pentagon has five sides, a hexagon has six sides, and an octagon has eight. Mathematicians use the term "n-agon" when referring to an "n"-sided polygon. There is no maximum value for the number of sides a polygon can have. A polygon can still be simple (when its sides don't intersect), like a square, or complex (when its sides intersect), like a star.

Step 2. Find out if the polygon that will be drawn should be regular

A regular polygon is one in which all angles and all sides are equal. It is important to remember that while this is the best known concept of a polygon, not all polygons are regular. Drawing a regular polygon requires a little more work than a simple polygon; if you want to learn how to draw one, research how to build regular polygons using a circle.

Method 1 of 3: Draw a Simple Polygon

Step 1. Make your job easier

A polygon does not have to be regular to be classified as a polygon. If you want to make your work easier, just use a ruler (or any other straight-sided material) and a pencil; draw line segments and connect them creating a closed shape. The result will be a polygon!

Unlike what most people believe, terms like "hexagon", "octagon" and "pentagon", for example, do not necessarily mean that the polygon is regular. "Hexagon" is the name given to a six-sided polygon; a "regular hexagon" has six equal sides and also six equal internal angles

Step 2. Always close the figure

Whether simple or complex, the line segments that make up a polygon must always form a circuit, that is, there must be no open space between them. If the sides are straight and form a closed figure, it will be a polygon!

Step 3. Study the properties of your polygon

To better understand the characteristics of the polygon, try calculating its perimeter or area.

Method 2 of 3: Draw a regular polygon

Step 1. Understand what a regular polygon is

A polygon classified as regular is one where all sides and all angles have the same measurement. The easiest regular polygons to identify are the equilateral triangle (it has three equal sides and interior angles measuring 60 degrees each) and the square (it has four equal sides and interior angles measuring 90 degrees each). Besides these, there are several other types of polygons that are much more complex!

Step 2. Decide which type of regular polygon will be drawn

When choosing a regular polygon (or a polygon of any other type) to draw, you'll have a vast list of options. For example:

• You can draw regular polygons using a circle.
• You can draw a square.
• You can draw a regular pentagon (five sides and five equal angles).
• You can draw a regular hexagon (six sides and six equal angles).
• You can draw a regular octagon (eight sides and eight equal angles).
• You can draw a polygon with as many sides/angles as you like! Note the following method to learn how to build regular polygons using a circle.

Method 3 of 3: Draw a regular polygon with protractor

Step 1. Draw a circle on the paper using the protractor

Since the protractor is shaped like a semi-circle, start by drawing a straight line with the straight part of the protractor. Mark the middle and ends of the straight line with dots. Then use the curved part of the protractor to draw a semi-circle (starting from one end of the straight line until reaching the other) and then turn it to draw another semi-circle (aligning with the points in the center and at the ends of the straight line) then forming a complete circle.

Step 3. Calculate the value of the center angle formed by the lines running from the center to the adjacent vertices

A circle has a total of 360 degrees, so just divide that 360 degrees by the number of sides of the polygon (which is equal to its number of vertices). The resulting value of this operation is the measure of the angle formed between two straight lines coming from the center of the circle to two adjacent vertices of the polygon.

For example, if you are going to draw a hexagon, the value of this angle is 60 degrees

Step 4. Use the protractor to mark the angle measurement

Choose a starting point and, from there, turn the protractor (clockwise or counterclockwise) and mark with a point the measurement of the angle calculated in the previous step until completing one revolution.

For example, if you are going to draw a hexagon, start by choosing a place on the circle to mark the first point; then, using the protractor, mark the next point 60 degrees from the first. Repeat this process until you have scored all six points

Step 5. Connect adjacent dots with a straight line

Do this with a ruler being careful not to overlap the lines. Make dashed lines before drawing the sides of the polygon definitively; this will make it easier to erase and correct any errors or overlapping lines.

Step 6. Erase the dashed lines and circle

Your polygon is ready! To make sure it's really regular, check with the ruler that all the straight segments (that is, the sides of the polygon) are the same length.