math

posted by .

A drawing of diagonals for four different polygons is listed below. What is the number of diagonals for a 100-sided polygon?

• math -

100 sided polygon has = n(n-3)/2 diagonals

100(100-3)/2
4850 diagonals

• math -

The number of diagonals in the first series of polygons are

Number of sides...........n = 3....4....5....6....7....8
Number of diagonals.....N = 0....2....5....9...14..20
1st Difference.......................2....3....4....5....6
2nd Difference.........................1....1....1....1

We therefore, have a finite difference sequence with the 2nd differences constant at 1. This means that the general expression for the number of diagonals in any n-gon is of the form N = an^2 + bn + c.

Using the data, we can write
a(3^2) + b(3) + c = 0 or 9a + 3b + c = 0
a(4^2) + b(4) + c = 2 or 16a + 4b + c = 2
a(5^2) + b(5) + c = 5 or 25a + 5b + c = 5

Solving this set of equations leads us to a = 1/2, b = -3/2, and c = 0 resulting in N = n^2/2 - 3n/2 = n(n - 3)/2.

Similar Questions

1. math

What polygon has 20 diagonals?I don't know how to figur this out. THANKS!!!! A rectangle (4 sides) has 2 diagonals. A hexagon (6 sides) has 3 diagonals. An octagon (8 sides) has 4 diagonals. A _____ (20 sides) has 20 diagonals.
2. Algebra

I can't find the formula for the sides of a polygon vs. the total diagonals that it has! ex: 3 sided polygon, 0 diagonals, 4 sided, 2 diags, 5 s, 5 d, 6 s, 9 d, 7 s, 14 d 8 s, 20d, etc. someone please tell me the formula http://mathforum.org/library/drmath/view/54874.html
3. math

louis drew all of the possible diagonals from one vertex of a regular hexagon. Which of these statements is true?
4. geometry

If a polygon is a kite, which statement is not true?
5. geometry

A polygon has d diagonals. If the polygon had one more side, it would d + 10 diagonals. How many sides does the polygon have?
6. Identifying patterns

If the pattern of polygons continues, how many sides will polygon 98 have?