A formula is a rule in letters
A ribbon goes round the edge of a hexagon. Each side is 7 cm. How long is the ribbon?
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Slide the number of sides. Six sides give 6a. Eight sides give 8a.
A hexagon has 6 sides, each 7 cm. The ribbon is the perimeter: the length all the way round. So it is 6 × 7 = 42 cm.
The rule
A formula is a rule written in letters. A regular polygon has equal sides and equal angles. With n sides of length a, its perimeter is n × a.
| Shape | Sides | Formula | When a = 7 |
|---|---|---|---|
| Square | 4 | 4a | 28 |
| Hexagon | 6 | 6a | 42 |
| Octagon | 8 | 8a | 56 |
| Decagon | 10 | 10a | 70 |
For the ribbon, 6a is 6 × a. With a = 7, that is 6 × 7 = 42 cm.
One formula gives an answer for every side length. Change a, and the answer changes with it.