The first step we are going to take is to know the etymological origin of the term dodecagon that concerns us now. In this case, we can establish that it derives from the Greek, exactly from “dodekagonos”. This word, which means “geometric figure with twelve angles”, is the result of the sum of several lexical components of the aforementioned language:
-The noun “dodeka”, which is synonymous with “twelve”.
-The word “gonos”, which can be translated as “angles”.
The term dodecagon is used in the field of geometry to name a polygon that has twelve sides and twelve angles . A polygon, for its part, is a plane figure delimited by lines.
When one side of the dodecagon is extended and the entire figure is located in one of the semiplanes that determine the side in question and its extensions, it is a convex dodecagon . On the other hand, if the figure is located in both semiplanes, the dodecagon is concave .
The regular dodecagon , on the other hand, is one with interior angles that measure the same ( 150º ) and with sides of identical length. The external angles of the regular dodecagon, meanwhile, measure 30º . If we take into account that a dodecagon has twelve angles , and that the interior angles of a regular dodecagon measure 150º each, we can affirm that the sum of all the interior angles of a regular dodecagon is equal to 1800º ( 150º x 12 = 1800º ) .
Another characteristic of dodecagons is that they have 54 diagonals . This can be verified through the formula that indicates that the number of diagonals of a polygon is equal to the multiplication of its sides by its sides minus 3, dividing that result by two.
Diagonals of a polygon = No. of sides x (No. of sides – 3) / 2)
Diagonals of a dodecagon = 12 x (12 – 3) / 2
Diagonals of a dodecagon = 12 x 9 / 2
Diagonals of a dodecagon = 108 / 2
Diagonals of a dodecagon = 54
Other relevant data about the dodecagon are the following:
-The central angle of what is the regular dodecagon measures 30º.
-The area of the regular dodecagon is calculated by multiplying the diameter by the apothem and the result dividing it by two.
-To discover the perimeter of a regular dodecagon you have to multiply the length of one of its sides by twelve, which are the twelve sides it has.
-The irregular dodecagon is one that does not have all its sides and angles equal. Furthermore, it is important to know that it can be concave or convex.
-As for the irregular one, we can establish that its perimeter is calculated by adding the length of each and every one of its sides. If what you want is to know the area of that, the existing formula establishes that the best option is to divide the dodecagon into twelve triangles and then add the areas of each of those.
-In addition to everything established, we can indicate the existence of what is known as star dodecagons and even regular ones that are inscribed in a circle.