07/03/2020
How to calculate diagonals of polygon by MathExame
Definition of diagonal:
A diagonal is a inclined line segment joining two angle of a polygon or polyhedra from inside.
Example:
In the following polygon image all colourful lines are diagonals.
For calculating diagonals of polygon we have to count the number of side.
Polygon
Polygon
Number of sides of polygon, n = 6
Formula for calculating diagonals of polygon , D= [n(n-3)]÷2
Putting n= 6 in step 2
D= [6(6-3)]÷2
D= [6×3]÷2
D= 18÷2
D= 9
Answer so above image have 9 diagonals.
Explanation of formula:-
Let's take an example n-sided polygon will have n vertices, and from each vertex you can draw n-3 diagonals, because you can't draw a diagonals right left and on that point you're starting. So the total number of diagonals that can be drawn is n(n-3).
This would mean that each diagonal would be drawn twice, (to and from each vertex), so the expression must be divided by 2.
