Quadrilateral/tetragon: 4 sides Pentagon: 5 sides Hexagon: 6 sides Heptagon: 7 sides Octagon: 8 sides Nonagon/Enneagon: 9 sides Decagon: 10 sides Hendecagon: 11 sides Dodecagon: 12 sides Triskaidecagon/tridecagon: 13 sides Tetrakaidecagon/tetradecagon: 14 sides Pentadecagon: 15 sides Hexadecagon: 16 sides Heptadecagon: 17 sides Octadecagon: 18 sides Enneadecagon: 19 sides Icosagon: 20 sides Note that a triangle has no diagonals. [3] X Research source
To draw the polygon, use a ruler and draw each side the same length, connecting all of the sides together. If you’re unsure what the polygon will look like, search for pictures online. For example, a stop sign is an octagon.
For a square, draw one line from the bottom left corner to the top right corner and another line from the bottom right corner to the top left corner. Draw diagonals in different colors to make them easier to count. Note that this method gets much more difficult with polygons that have more than ten sides.
For the square, there are two diagonals: one diagonal for every two vertices. A hexagon has 9 diagonals: there are three diagonals for every three vertices. An octagon has 20 diagonals. Past the heptagon, it gets more difficult to count the diagonals because there are so many of them.
For example, a pentagon (5 sides) has only 5 diagonals. Each vertex has two diagonals, so if you counted each diagonal from every vertex twice, you might think there were 10 diagonals. This is incorrect because you would have counted each diagonal twice!
A hexagon has 9 diagonals. A octagon has 20 diagonals.
This equation can be used to find the number of diagonals of any polygon. Note that the triangle is an exception to this rule. Due to the shape of the triangle, it does not have any diagonals. [10] X Research source
Tetra (4), penta (5), hexa (6), hepta (7), octa (8), ennea (9), deca (10), hendeca (11), dodeca (12), trideca (13), tetradeca (14), pentadeca (15), etc. For very large sided polygons you may simply see it written “n-gon”, where “n” is the number of sides. For example, a 44-sided polygon would be written as 44-gon. If you are given a picture of the polygon, you can simply count the number of sides.
For example: A dodecagon has 12 sides. Write the equation: n(n-3)/2 Plug in the variable: (12(12 - 3))/2
For example: (12(12 – 3))/2 Subtract: (12*9)/2 Multiply: (108)/2 Divide: 54 A dodecagon has 54 diagonals.
Hexagon (6 sides): n(n-3)/2 = 6(6-3)/2 = 63/2 = 18/2 = 9 diagonals. Decagon (10 sides): n(n-3)/2 = 10(10-3)/2 = 107/2 = 70/2 = 35 diagonals. Icosagon (20 sides): n(n-3)/2 = 20(20-3)/2 = 2017/2 = 340/2 = 170 diagonals. 96-gon (96 sides): 96(96-3)/2 = 9693/2 = 8928/2 = 4464 diagonals.
