How many diagonals does a 20 sided shape have?

Answer 1

A 20 sided shape has 209 diagonals i worked it out by drawing a table and split it into 4 colunms. I named the first one Name of polygon and the second one Number of sides the next one, Angle at centre and the last one Diagonals. I started with a Triangle which has 3 sides and its angle at centre is 120 degrees but, it doesn't have any diagonals so i put 0. Next i used a quadrilateral which has 4 sides and its angle at centre is 90 degrees and, it does have diagonals it has 2. Afterthat i put down a pentagon which has 5 sides its angle at centre is 72 degrees and it has 5 diagonals. I kept the process going so i put down Hexagon, Heptagon, Octagon, Nonagon and finally Decagon when, i had finished filling in the rest this was my results:

Hexagon= Had 6 sides its angle at centre 60 degrees and its diagonals 9

Heptagon= Had 7 sides its angle at centre 51.5 degrees and its diagonals 14

Octagon= Had 8 sides its angle at centre 45 degrees and its diagonals 20

Nonagon= Had 9 sides its angle at centre 40 degrees and its diagonals 27

Decagon= Had 10 sides its angle at centre 36 degrees and its diagonals 35

this is my results just for Diagonals

Triangle=0

Quadrilateral=2

Pentagon=5

Hexagon=9

Heptagon=14

Octagon=20

Nonagon=27

Decagon=35

Can you see a pattern?

well i can see a pattern that adds a different number every time which is:

1. it adds 2
2. it adds 3
3. it adds 4
4. it adds 5
5. it adds 6
6. it adds 7
7. it adds 8
8. it adds 9

so for a 20 sided shape you need to take 35 and add on 10 etc to 20. This is my results:

35 + 9 = 44

44 + 10 = 54

54 + 11 = 65

65 + 12 = 77

77 + 13 = 90

90 + 14 = 104

104 + 15 = 119

119 + 16 = 135

135 + 17 = 152

152 + 18 = 170

170 + 19 = 189

189 + 20 = 209

So the answer is 209 diagonals on a 20 sided shape :-P