The pattern shows a sequence of triangles constructed using straws. The total number of small triangles formed and the total number of straws used for the first three patterns are shown on the table.
- Find the number of small triangles in Figure 4.
- Find the number of small triangles in Figure 22.
- Find the number of straws in Figure 42.
Figure |
1 |
2 |
3 |
4 |
22 |
42 |
Number of small triangles |
1 |
4 |
9 |
(a) ? |
(b) ? |
|
Number of straws |
3 |
9 |
18 |
... |
|
(c) ? |
(a)
Pattern for the number of small triangles
Figure 1: 1
2 = 1
Figure 2: 2
2 = 4
Figure 3: 3
2 = 9
Formula
Number of small triangles = Figure number
2 Number of small triangles for Figure 4
= 4
2 = 16
(b)
Number of small triangles for Figure 22
= 22
2 = 22 x 22
= 484
(c)
Patterns for the number of straws
Figure 1: 3 x (1)
Figure 2: 3 x (1 + 2)
Figure 3: 3 x (1 + 2 + 3)
Formula
Number of straws = 3 x [Figure Number x (Figure number + 1) ÷ 2]
Number of straws in Figure 42
= 3 x (42 x (42+1) ÷ 2)
= 3 x (42 x 43 ÷ 2)
= 3 x (1806 ÷ 2)
= 3 x 903
= 2709
Answer(s): (a) 16; (b) 484; (c) 2709