an octagon has 8 sides. how many diagonal does an octagon have
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)
To find the number of diagonals in an octagon, we need to consider the formula.
The formula for calculating the number of diagonals in a polygon is:
n(n-3)/2,
where n is the number of sides.
In the case of an octagon, which has 8 sides, we can substitute the value of n into the formula:
8(8-3)/2 = 8(5)/2 = 40/2 = 20.
Therefore, an octagon has 20 diagonals.