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Do you know, the word "polygon" is a generic name for most geometrical shapes. That means, out there, there are so many polygons that need to be distinguished from one another. However, before categorizing polygons into their types, let's learn about polygons. This topic is very lengthy and that is why in this resource, we will tell you a summarized version of a polygon. However, if you want to learn more, you can always click the link to learn that topic in detail.
Polygon
A polygon is a geometrical figure that contains at least 3 sides. These sides are straight lines, which means any other lines such as curve lines, etc. are out of the box. Each line is joined from both sides to another line. Does that mean a polygon can have more than 3 sides, for example, let's say 5 sides? Yes, if all the lines are straight and are attached from each side. So, we have 3 conditions for a polygon.
- Straight lines
- At least three sides
- All corners are joined, leaving no empty spaces
There are different rules for a polygon, in fact, there are six rules of a polygon.
- Convex polygon
- Concave polygon
- Equilateral polygon
- Equiangular polygon
- Regular polygon
- Irregular polygon
Sides of a Polygon
The sides of a polygon change the whole scenario. Adding or removing the side results in changing the whole geometric figure that means changing everything from its properties to its application. There is no fixed number of how many sides a polygon can have. In short, there can be infinite numbers of sides, however, the more the sides, the closer it will get to the circle and we all know a circle is not a polygon. Consider "Icosagon". It has 20 sides and it does resemble a lot with a circle. We can't say it is a circle because it has edges and on each edge, there is an angle, unlike a circle that doesn't have a single edge on its boundary.
Height of a Polygon
Looking at different shapes of polygon makes a person think that finding height would be very difficult, some might agree but we don't. We have a very simple method for finding the height of a polygon but calculating the height of a polygon, is a problem. Let's first find the height and then worry about its calculation. The rule is simple, you need to find the base of the polygon. The next step is to find the top-most vertex of the polygon. Now draw a line starting from the base of the polygon to the vertex to the opposite side (or its extension) of the polygon.
Diagonals of a Polygon
Diagonal is a line segment between two non-consecutive vertices. The type and sides of a polygon determine the number of diagonals. Almost all polygons contain at least one diagonal except triangles. Making diagonals are easy, all you need to do is to connect vertices with each other using a straight line. However, calculating the number of diagonals is another thing. For more detail about calculations, click on the link.
Apothem
Apothem is the distance between the centre of a polygon to one of its side's midpoint. To find the apothem of a polygon, you need to find its centre first. Draw a straight line from the centre to one of the polygon's sides and make sure the line is perpendicular to the side. Sometimes apothems are very easy to calculate such as apothem of a square, rectangle, sometimes it can be very difficult too such as apothem of hexagon, etc.
Medians
Polygons also have medians of every side. The number of sides decides the number of medians a polygon has. A Median is a line that crosses the centre of a side and joins at the vertex. This concept is very useful for determining the centre of a polygon. The famous application of the median is the centroid of a triangle.
Angles of a Polygon
Like every other geometrical shape, polygons also consists of angles. As the number of sides increases, the angles also increases. There are two types of angles, interior angle and exterior angle. Interior angle is the angle that is created by a vertex of a polygon. However, an exterior angle is formed with the help of the extended adjacent side. The exterior angle is the angle between the side and the extended side of the polygon. The sum of both angles will always be equal to 
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Area and Perimeter of Polygons
As the number of sides and angles changes, the area and perimeter of the polygon change. In short, the area and perimeter depend on the number of sides and type of a polygon. Each polygon has a different structure, therefore, there is not a simple formula for finding the area of the polygon. However, you might find the perimeter easier. To find the perimeter of a polygon, you need to add all the sides. Whether it is a triangle or an octagon, you can find the perimeter by adding all its sides but don't add the diagonal in it because diagonal is not a part of the perimeter.
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I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html