Each figure is made up of a number of identical rods of 1-cm length.
- Find the perimeter of Figure 76.
- Find the number of rods in Figure 108.
- Given that a figure has a perimeter, P, of 410 cm, find the number of squares in this figure.
Figure Number |
Number of squares |
Number of triangles |
Perimeter (P) |
Number of rods |
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 76
= 76 x 4 + 2
= 306 cm
(b)
Pattern for the number of rods
Figure 1: 1 x 7 + 1 = 8
Figure 2: 2 x 7 + 1 = 15
Figure 3: 3 x 7 + 1 = 22
Number of rods = Figure number x 7 + 1
Number of rods in Figure 108
= 108 x 7 + 1
= 757
(c)
Perimeter = Figure number x 4 + 2
Figure number = (Perimeter - 2) ÷ 4
Figure number with the perimeter 410 cm
= (410 - 2) ÷ 4
= 408 ÷ 4
= 102
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 102 = 102
Answer(s): (a) 306 cm; (b) 757; (c) 102