Regular Polygon Area
A regular polygon splits into n isosceles triangles from the centre. More sides means more area for the same perimeter, approaching a circle in the limit.
Your numbers
Area
259.81cm²
Perimeter
60cm
Interior angle
120°
Formula
Area = Number of sides × Side length² ÷ (4 × tan(π ÷ Number of sides))
A hexagon with 10 cm sides is 259.81 cm². A square of the same perimeter (15 cm sides) is only 225 cm².
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Number of sidesHow many sides the polygon has, counting from three. | 6 | 3 ~ 100 |
| Side length (cm)One side of a regular polygon — they are all the same. | 10 | 0 and up |
Step by step
Quick reference table
Results when only Number of sides changes and everything else stays put.
| Number of sides | Area (cm²) | Perimeter (cm) | Interior angle (°) |
|---|---|---|---|
| 3 | 43.3 | 30 | 60 |
| 4.5 | 172.05 | 50 | 108 |
| 6 | 259.81 | 60 | 120 |
| 9 | 618.18 | 90 | 140 |
| 12 | 1,119.62 | 120 | 150 |
What each result means
| Result | At default values |
|---|---|
| Area (cm²)The space a shape covers — length squared. | 259.81 |
| Perimeter (cm)The total length around the outside of a shape. | 60 |
| Interior angle (°)The interior angle at one corner of a regular polygon. | 120 |
Common mistakes
A hexagon with 10 cm sides is 259.81 cm². A square of the same perimeter (15 cm sides) is only 225 cm².
Glossary
- Number of sides
- How many sides the polygon has, counting from three.
- Side length
- One side of a regular polygon — they are all the same.
- Area
- The space a shape covers — length squared.
- Perimeter
- The total length around the outside of a shape.
- Interior angle
- The interior angle at one corner of a regular polygon.
Frequently asked questions
Q. How is Regular Polygon Area calculated?
Area = Number of sides × Side length² ÷ (4 × tan(π ÷ Number of sides)) — A regular polygon splits into n isosceles triangles from the centre. More sides means more area for the same perimeter, approaching a circle in the limit.
Q. Can you walk through an example?
With Number of sides 6, Side length 10cm, the answer is Area 259.81cm².
Q. What do I need to enter?
Enter Number of sides, Side length. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Number of sides moves the answer to Number of sides 3 → Area (cm²) 43.3 and Number of sides 12 → Area (cm²) 1,119.62. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
A hexagon with 10 cm sides is 259.81 cm². A square of the same perimeter (15 cm sides) is only 225 cm².
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.