Each of the figures is made up of 1-cm matchsticks.
The table shows the number of matchsticks used to make the figures and their perimeters.
- Find the number of matchsticks in Figure 14.
- What is the perimeter of Figure 192?
- Which figure requires a total number of 1311 matchsticks?
(a)
Pattern for the number of matchsticks
Figure 1: 1 x 8 + 7 = 15
Figure 2: 2 x 8 + 7 = 23
Figure 3: 3 x 8 + 7 = 31
Formula:
Number of matchsticks = Pattern number x 8 + 7
Number of matchsticks in Figure 14
= 14 x 8 + 7
= 119
(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 192
= 192 x 2 + 7
= 391
(c)
Figure number x 8 + 7 = 1311
Figure number x 8 = 1311 - 7 = 1304
Figure number = 1304 ÷ 8 = 163
Answer(s): (a) 119; (b) 391; (c) 163