How to Find How Many Diagonals Are in a Polygon
Know the names of polygons., Draw the polygon., Draw the diagonals., Count the diagonals., Beware of counting a diagonal more than once., Practice with some examples.
Step-by-Step Guide
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Step 1: Know the names of polygons.
You may need to first identify how many sides are present in the polygon.
Each polygon has a prefix that indicates the number of sides it has.
Here are the names of polygons with up to twenty sides:
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 Pendedecagon: 15 sides Hexdecagon: 16 sides Heptdecagon: 17 sides Octdecagon: 18 sides Enneadecagon: 19 sides Icosagon: 20 sides Note that a triangle has no diagonals. -
Step 2: Draw the polygon.
If you wanted to know how many diagonals were present in a square, you would start by drawing the square.
The easiest way to find diagonals and count them is to draw the polygon symmetrically, each side has the same length.
It’s important to note that even if the polygon is not symmetrical, it will still have the same number of diagonals.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. , A diagonal is a line segment drawn from one corner of the shape to another, excluding the sides of the polygon.Starting at one vertex of the polygon, use a ruler to draw a diagonal to every other available vertex.
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. , There are two options for counting: you can count as you draw the diagonals or count them once they have been drawn.
As you count each diagonal, draw a small number above the diagonal to denote that it has been counted.
It is easy to lose track while counting when there are a lot of diagonals crossing each other.
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.
A heptagon has 14 diagonals.
Past the heptagon, it gets more difficult to count the diagonals because there are so many of them. , Each vertex may have multiple diagonals, but that doesn’t mean that the number of diagonals is equal to the number of vertices times the number of diagonals.
Take care when counting the diagonals to count each one only once.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! , Draw some other polygons and count the number of diagonals.
The polygon does not have to be symmetric for this method to work.
In the case of a concave polygon, you may have to draw some of the diagonals outside the actual polygon.A hexagon has 9 diagonals.
A heptagon has 14 diagonals. -
Step 3: Draw the diagonals.
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Step 4: Count the diagonals.
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Step 5: Beware of counting a diagonal more than once.
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Step 6: Practice with some examples.
Detailed Guide
You may need to first identify how many sides are present in the polygon.
Each polygon has a prefix that indicates the number of sides it has.
Here are the names of polygons with up to twenty sides:
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 Pendedecagon: 15 sides Hexdecagon: 16 sides Heptdecagon: 17 sides Octdecagon: 18 sides Enneadecagon: 19 sides Icosagon: 20 sides Note that a triangle has no diagonals.
If you wanted to know how many diagonals were present in a square, you would start by drawing the square.
The easiest way to find diagonals and count them is to draw the polygon symmetrically, each side has the same length.
It’s important to note that even if the polygon is not symmetrical, it will still have the same number of diagonals.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. , A diagonal is a line segment drawn from one corner of the shape to another, excluding the sides of the polygon.Starting at one vertex of the polygon, use a ruler to draw a diagonal to every other available vertex.
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. , There are two options for counting: you can count as you draw the diagonals or count them once they have been drawn.
As you count each diagonal, draw a small number above the diagonal to denote that it has been counted.
It is easy to lose track while counting when there are a lot of diagonals crossing each other.
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.
A heptagon has 14 diagonals.
Past the heptagon, it gets more difficult to count the diagonals because there are so many of them. , Each vertex may have multiple diagonals, but that doesn’t mean that the number of diagonals is equal to the number of vertices times the number of diagonals.
Take care when counting the diagonals to count each one only once.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! , Draw some other polygons and count the number of diagonals.
The polygon does not have to be symmetric for this method to work.
In the case of a concave polygon, you may have to draw some of the diagonals outside the actual polygon.A hexagon has 9 diagonals.
A heptagon has 14 diagonals.
About the Author
Carol Rivera
Enthusiastic about teaching organization techniques through clear, step-by-step guides.
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