A polygon is a shape of plane geometry. It’s made of straight lines connected to each other forming a “closed” shape.
Polygon comes from the Greek words ”poly”, meaning “many”, and “gonia”, meaning "angles". So it’s a shape with many angles.
Types of polygons
There are several types of polygons.
Here are the most typical of them:
|All angles are less than 180˚||One or more angles are |
more than 180˚.
|All angles and sides are |
|Not all angles and sides are |
The angle sum of a convex polygon with n sides is given by:
Triangles and rectangles are typical examples of convex polygons.
Let’s try to calculate the angle sum of the these two shapes with the formula above:
Regular polygons are the only polygons of which it’s possible to make general formulas applicable to all of them.
The circumference of a regular polygon
where C is the circumference, n is the number of sides, and b is the side length.
The area of a regular polygon
Where A is the area, n is the number of sides, and b is the side length.
Use the following formula instead, if your calculator hasn't got the cotangent feature.
Names of polygons
A polygon is named after its number of vertices.
|Trigon||Triangle||180||The triangle is an important shape in triangulation.|
Triangulation was used in the old days to
determine locations and to create maps.
|Tetragon||Quadrilateral||360||A football field|
|Pentagon||5-sided shape||540||The headquarters of the United States |
Department of Defense
|Hexagon||6-sided shape||720||The hexagon is common in nature and in chemistry,|
for example the pattern you see inside a beehive
or the structure of sugar molecules.
|Heptagon or septagon||7-sided shape||900||British coins: 20 and 50 pence.|
|Octagon||8-sided shape||1080||Stop sign in traffic.|