Login

what is the formula used for finding out the diagnols of a polygon?

Definition: The diagonal of a polygon is a line segment linking two non-adjacent vertices. Try this Adjust the number of sides of the polygon below, or drag a vertex to note the behavior of the diagonals.

Diagonals of a Polygon From Greek: dia- "across" + -gonia "angle," Definition: The diagonal of a polygon is a line segment linking two non-adjacent vertices. Try this Adjust the number of sides of the polygon below, or drag a vertex to note the behavior of the diagonals.

A diagonal of a polygon is a line segment joining two vertices. From any given vertex, there is no diagonal to the vertex on either side of it, since that would lay on top of a side. Also, there is obviously no diagonal from a vertex back to itself. This means there are three less diagonals than there are vertices. (diagonals to itself and one either side are not counted).

Formula for the number of diagonals

As described above, the number of diagonals from a single vertex is three less than the the number of vertices or sides, or (n-3).

There are N vertices, which gives us n(n-3) diagonals

But each diagonal has two ends, so this would count each one twice. So as a final step we divide by 2, for the final formula:

wher n is the number of sides (or vertices)

  • 2
View Full Answer
Steps
  1. 1Identify your polygon. The number of diagonals increases quadratically as the number of sides in a polygon, so even a minor change from a enneadecagon (19 sided polygon) to an icosagon (20-sided polygon) could be an answer to the test, so be careful about it.

Method 1 of 3: Novice Method
  1. 1Draw every single possible line from one vertex to another. This will help you understand the concept of diagonals.
  2. 2 Count. Unfortunately, along with the diagram, you will have to count every single line to figure out how many diagonals are in a polygon. This can be stressful if you are working on a polygon that has more than 12 sides. If you are working with a simple square, you can see where the term "diagonal" comes from.

Method 2 of 3: Advanced Method
  1. 1Know how to simplify terms. This is because a formula is involved in this situation.
  2. 2Use the formula (n² - 3n)/2. "n" represents the sides of a polygon, so if you had a pentagon and you wanted to figure out the diagonals, insert "5" for n. The result will become:
    • 1. (5² - 3(5))/2
    • 2. (25 - 15)/2
    • 3. 10/2
    • 4. The number of diagonals for a pentagon is 5.
    • This formula is not easy to memorize as you will not use it as often as others. However, this should still be committed to memory as it gets particularly useful in everyday life. Make sure that you do the subtraction first, then the division. To prove this, use the novice method.

Method 3 of 3: More Examples
  • Hexagon (6 sides)
    • 1. (6² - 3(6))/2
    • 2. (36 - 18)/2
    • 3. 18/2
    • 4. There are 9 diagonals.
  • Decagon (10 sides)
    • 1. (10² - 3(10))/2
    • 2. (100 - 30)/2
    • 3. 70/2
    • 4. There are 35 diagonals.
  • Icosagon (20 sides)
    • 1. (20² - 3(20))/2
    • 2. (400 - 60)/2
    • 3. 340/2
    • 4. There are 170 diagonals.
  • 96-gon (the polygon Archimedes used to find the approximate value of Pi)
    • 1. (96² - 3(96))/2
    • 2. (9216 - 288)/2
    • 3. 8928/2
    • 4. There are 4464 diagonals.

  • 1
What are you looking for?