Thread: Hexagon combination problems

Sketch a regular Hexagon
I.) how many lines can be connecting two points on the hexagon, including sides of the hexagon( was able to work this one out to be 15)
II.) How many of these lines are diagonals of the hexagon(9)
III.) Express the answer to (II) in terms of combinations.
d.) how many diagonals are there in a regular pentagon? octagon? decagon?(5,20,35)
e.) how many diagonals are ther ein regular "n" sided polygon?

Any help or solutions would be helpful

Originally Posted by nightrider456

Sketch a regular Hexagon
I.) how many lines can be connecting two points on the hexagon, including sides of the hexagon( was able to work this one out to be 15)
II.) How many of these lines are diagonals of the hexagon(9)
III.) Express the answer to (II) in terms of combinations.
d.) how many diagonals are there in a regular pentagon? octagon? decagon?(5,20,35)
e.) how many diagonals are ther ein regular "n" sided polygon?

Any help or solutions would be helpful

Hint for III: How many pairs of vertices are there? Are the lines connecting pairs of vertices all diagonals? If not, can you count the lines that are not diagonals?