Each figure is made up of a number of identical sticks of 1-cm length.
- Find the perimeter of Figure 71.
- Find the number of sticks in Figure 112.
- Given that a figure has a perimeter, P, of 274 cm, find the number of squares in this figure.
Figure Number |
Number of squares |
Number of triangles |
Perimeter (P) |
Number of sticks |
1 |
1 |
2 |
6 |
8 |
2 |
2 |
4 |
10 |
15 |
3 |
3 |
6 |
14 |
22 |
4 |
4 |
8 |
18 |
... |
... |
... |
... |
... |
... |
8 |
... |
... |
... |
... |
(a)
Pattern for perimeter in cm
Figure 1: 1 x 4 + 2 = 6
Figure 2: 2 x 4 + 2 = 10
Figure 3: 3 x 4 + 2 = 14
Perimeter = Figure number x 4 + 2
Perimeter for Figure 71
= 71 x 4 + 2
= 286 cm
(b)
Pattern for the number of sticks
Figure 1: 1 x 7 + 1 = 8
Figure 2: 2 x 7 + 1 = 15
Figure 3: 3 x 7 + 1 = 22
Number of sticks = Figure number x 7 + 1
Number of sticks in Figure 112
= 112 x 7 + 1
= 785
(c)
Perimeter = Figure number x 4 + 2
Figure number = (Perimeter - 2) ÷ 4
Figure number with the perimeter 274 cm
= (274 - 2) ÷ 4
= 272 ÷ 4
= 68
Pattern for the number of squares
Figure 1: 1
Figure 2: 2
Figure 3: 3
Number of squares = Figure number
Number of squares for Figure 68 = 68
Answer(s): (a) 286 cm; (b) 785; (c) 68