Mathematics
Look at the following matchstick pattern of polygons. Complete the table. Also write the general rule that gives the number of matchsticks.
| Number of polygons | 1 | 2 | 3 | 4 | 5 | … | n |
|---|---|---|---|---|---|---|---|
| Number of matchsticks | … | … | … | … | … | … | … |
Answer
Each polygon (house-shape) is formed using 5 matchsticks. Two neighbouring polygons have one common matchstick. So, for every new polygon added after the first, 4 more matchsticks are required.
| Number of polygons | 1 | 2 | 3 | 4 | 5 | … | n |
|---|---|---|---|---|---|---|---|
| Number of matchsticks | 5 | 9 | 13 | 17 | 21 | … | 4n + 1 |
Observe that:
5 = 4 × 1 + 1
9 = 4 × 2 + 1
13 = 4 × 3 + 1
17 = 4 × 4 + 1
21 = 4 × 5 + 1
Hence, the general rule that gives the number of matchsticks is 4n + 1, where n is the number of polygons.
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