Perimeter of a Regular Polygon
Total length around a regular polygon.
Formula
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Example
Hexagon s=3 → P = 18
How it works
A regular polygon has all sides the same length, so its perimeter is just the sum of those equal sides. If there are n sides and each side has length s, adding s n times gives P = n s. This works only for regular polygons, because irregular polygons may have different side lengths and need each side added separately.
When to use it
Use this when you know the number of equal sides in a regular shape, such as a regular pentagon, octagon, or decagon. It is common in geometry problems, design, tiling, and any task where you need the total boundary length of a symmetric polygon.
Worked example, step by step
A regular octagon has side length 4 cm. Use P = n s P = 8 × 4 P = 32 cm So, the perimeter is 32 cm.
Common mistakes to avoid
- Using this formula for an irregular polygon with unequal sides
- Forgetting to multiply by the number of sides and only writing the side length
- Mixing up perimeter with area
Did You Know?
As you add sides to a regular polygon, it looks more and more like a circle — the basis of Archimedes' π estimate.
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