The figure shows a 5-sided figure with diagonal lines drawn within it.
- Complete the table.
- Find the number of diagonals of a figure with 13 sides.
(a)
Pattern for the number of diagonals
3 sides: 0 diagonal = 0
4 sides: 2 diagonals = 1 + 1
5 sides: 5 diagonals = 2 + 2 + 1
6 sides: 9 diagonals = 3 + 3 + 2 + 1
Formula:
Number of diagonals = (Number of sides - 3) +
last digit x (last digit + 1)2 Number of diagonals in a figure with 10 sides
= (10 - 3) +
7 x 82 = 35
(b)
Number of diagonals in a figure with 13 sides
= (13 - 3) +
10 x 112= 65
Answer(s): (a) 35; (b) 65
