Polygons in Geometry

Updated: Jun 22, 2021

Dear students of Math Lobby, we will be covering the topic on Polygons in Geometry today. Do check out our other articles Geometry articles namely Angles in Geometry, Triangles in Geometry and Special Quadrilaterals in Geometry if you have not done so. Without further ado, let’s begin!

In this note, you will learn:

1. What are polygons?

2. Types of polygons and its properties

3. Angles involving polygons (Exterior and interior)

1. What are polygons?

Polygons are defined to be plane figures with at least three or more straight sides, but typically five and above. It can be further categorized into regular polygons and irregular polygons, but we will be focusing on just regular polygons today. Circles, any shapes that includes a curve, any shape that is not closed and three-dimensional objects cannot be counted as polygons.

©Photo image from skillsyouneed

Types of polygons and its properties

As mentioned above, we will only be touching regular polygons today as stated in the SEAB syllabus. The types of polygons we will be going through are: Pentagon (5-sided), Hexagon (6-sided), Heptagon (7-sided), Octagon (8-sided), Nonagon (9-sided) and Decagon (10-sided).

As you can see from the diagram above, these polygons are called regular polygons, which means that they each have 1) sides of equal length and 2) identical angles at every vertex within the polygon. The general rule of thumb for the sum of interior angles in a polygon and the interior angle at each vertex of a polygon is given by:

Sum of interior angles = (n - 2) x 180°

Interior angle at each vertex of a polygon = [(n – 2) x 180°] / n

where n = number of sides of the polygon

Question Time!

Can you find the sum of interior angles and interior angle at each vertex of a 52-sided polygon? Leave your answer in the comments down below!