Each of the figures is made up of 1-cm toothpicks.
The table shows the number of toothpicks used to make the figures and their perimeters.
- Find the number of toothpicks in Figure 19.
- What is the perimeter of Figure 107?
- Which figure requires a total number of 1623 toothpicks?
(a)
Pattern for the number of toothpicks
Figure 1: 1 x 8 + 7 = 15
Figure 2: 2 x 8 + 7 = 23
Figure 3: 3 x 8 + 7 = 31
Formula:
Number of toothpicks = Pattern number x 8 + 7
Number of toothpicks in Figure 19
= 19 x 8 + 7
= 159
(b)
Pattern for the perimeter of the figure
Figure 1 = 1 x 2 + 7 = 9
Figure 2 = 2 x 2 + 7 = 11
Figure 3 = 3 x 2 + 7 = 13
Formula:
Perimeter of the figure = Pattern number x 2 + 7
Perimeter of figure 107
= 107 x 2 + 7
= 221
(c)
Figure number x 8 + 7 = 1623
Figure number x 8 = 1623 - 7 = 1616
Figure number = 1616 ÷ 8 = 202
Answer(s): (a) 159; (b) 221; (c) 202