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The word "Pentagon" can be broken into two parts, one is the "Pent" and the other is the "gon". The word, "Pent", is a Greek word that means five while the other word, "gon", is a part of the word "Polygon". In simple words, a Pentagon is a type of polygon that have five sides. You might be thinking that a regular pentagon is another name of a pentagon, if you are then, unfortunately, you are wrong. A pentagon can be a regular pentagon, want to find how? Keep on reading to find the difference between a regular pentagon and a pentagon.
What is a Regular Pentagon?
In order for a shape to be a pentagon, it should have five sides and five vertices too. The length of the sides doesn't matter. However, for a regular pentagon, all the lengths of the pentagon should be the same. Therefore, a regular pentagon is a polygon that has five sides and all sides are equal in length.
A regular pentagon is a polygon with five equal sides and angles. You can construct triangles by joining the centre with all vertices. If you are working with a regular pentagon that means all the triangles formed by the vertices and centre of the pentagon will be the same. Not to mention a regular pentagon is a convex geometrical shape. It means all the points of a regular pentagon will be pointing outside.
Angles of the Pentagon
All the angles inside of a regular pentagon are the same. The sum of all interior angles of a regular pentagon will be 
. That means that the angle on each vertex of a regular pentagon will be 
. Let's see how we found out that:
The sum of interior angles of a pentagon = 
The value of an interior angle of a regular pentagon is: 
The central angle of a regular pentagon measures: 
Diagonals of the Pentagon
A diagonal is a line that joins two non-adjacent vertices. A regular pentagon has 5 diagonals.
The number of diagonals in a regular pentagon = 
Apothem of the Regular Pentagon
Apothem is the distance of a line segment that is drawn from the centre of the polygon to the centre of any side of the regular pentagon. Let's calculate the apothem of a regular pentagon.
The first step is to draw the apothem as we did in the above diagram. If we draw another line segment from the centre of the regular pentagon to the vertex near to apothem, we could make a triangle. The best part of this triangle is that we can use the Pythagorean theorem to find the apothem of the regular pentagon. The line segment is equal to the side in length.
Perimeter of a Regular Pentagon
The perimeter of a regular pentagon shows the total length of the regular pentagon. To find the perimeter, you need to add all the sides of the regular pentagon. It means you need to add all five sides of the regular pentagon. Since a regular pentagon has all sides equal, we can conclude that:
Area of a Regular Pentagon
The area of a regular pentagon means the total space acquired by a regular pentagon. It is the half product of perimeter and apothem.
Example
Calculate the apothem, perimeter and area of a regular pentagon with a side of 6 cm.
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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