Alex wanted to find a pattern to predict the total number of
diagonals in a convex polygon. He used each of the figures
to the left to determine the number of diagonals in the 4-sided
convex polygon and the 5-sided convex polygon.
The table shows the relationship between the number
of sides, the number of diagonals drawn from each vertex, and the
total number of diagonals in each of the convex polygons listed in
the table.
Which expression represents the total number of diagonals for a
convex polygon with n sides?
Number of sides (n)
4
5
6
7
8
Number of diagonals from each
vertex (d)
1
2
3
4
5
Total number of diagonals
(t)
2
5
9
14
20
1Correct, good job!Student answered correctly.2Sorry, that's not right. Although this expression
works for a polygon with 5 sides, it does not work in general.
Consider a polygon
with 6 sides, which has 9 total diagonals. The expression you selected evaluates to
(5 * 2) + 1 = 11 total diagonals, which is incorrect. The correct answer is (n*d)/2.Student just checked the first pair.3Sorry, that's not right. Although this expression
works for a polygon with 5 sides, it does not work in general. It has to work for
all of the examples. The correct answer is (n*d)/2.Not sure what the student did.4Sorry, that's not right. Consider a polygon with
6 sides, which has 9 total diagonals. The expression you selected evaluates to
6 * 3 = 18 total diagonals, which is incorrect. The correct answer is (n*d)/2.Seems like a guess.TableOtherRecursiveExplicitOtherRecursiveVisualOtherRecursive