Asked by sophie
an octagon has 8 sides. how many diagonal does an octagon have
Answers
Answered by
Reiny
A triangle has 0 diagonals
A quadrilateral has 2 diagonals
A pentagon has 5 diagonals
A hexagon has 9 diagonals
Can you see a pattern ???
or, think of it this way
A hexagon has 6 vertices.
Joining any 2 of those 6 will produce either a side or a diagonal
The number of possible lines I can draw is C(6,2)
(choose any two points from the 6), which would be 15
But that would include the 6 original sides, so the rest or 9, must be diagonals.
Use the same argument for any n-gon
the number of diagonals for an n-gon would be
C(n,2) - n
(test this for my previous answers above)
A quadrilateral has 2 diagonals
A pentagon has 5 diagonals
A hexagon has 9 diagonals
Can you see a pattern ???
or, think of it this way
A hexagon has 6 vertices.
Joining any 2 of those 6 will produce either a side or a diagonal
The number of possible lines I can draw is C(6,2)
(choose any two points from the 6), which would be 15
But that would include the 6 original sides, so the rest or 9, must be diagonals.
Use the same argument for any n-gon
the number of diagonals for an n-gon would be
C(n,2) - n
(test this for my previous answers above)
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