Regular Polygon Area & Perimeter Calculator
Regular Polygon Area & Perimeter Calculator
A regular polygon has all sides and all angles equal - triangles, squares, pentagons, hexagons, and so on. Enter the number of sides and the side length, and this calculator finds the perimeter, the apothem (the distance from the center to the midpoint of a side), and the area, along with a diagram and the full step-by-step working.
- Perimeter = n × s, so a hexagon (n=6) with side 4 has a perimeter of 6 × 4 = 24 units.
- Apothem = s / (2 × tan(π/n)), the distance from the center to the middle of a side - for the same hexagon, that's 4 / (2 × tan(30°)) ≈ 3.46.
- Area = (Perimeter × Apothem) / 2, the same relationship used for any regular polygon, since it can be split into n identical isosceles triangles - for the hexagon, that's (24 × 3.46) / 2 ≈ 41.57.
How do I find the area of a regular polygon?
First find the apothem, then use Area = (Perimeter × Apothem) / 2. For a hexagon with side 4: perimeter 24, apothem ≈ 3.46, area ≈ 41.57.
What is an apothem?
The apothem is the perpendicular distance from the center of a regular polygon to the midpoint of any side - it's always shorter than the distance from the center to a vertex.
Regular Polygon Area & Perimeter Calculator
A regular polygon has all sides and all angles equal - triangles, squares, pentagons, hexagons, and so on. Enter the number of sides and the side length, and this calculator finds the perimeter, the apothem (the distance from the center to the midpoint of a side), and the area, along with a diagram and the full step-by-step working.
- Perimeter = n × s, so a hexagon (n=6) with side 4 has a perimeter of 6 × 4 = 24 units.
- Apothem = s / (2 × tan(π/n)), the distance from the center to the middle of a side - for the same hexagon, that's 4 / (2 × tan(30°)) ≈ 3.46.
- Area = (Perimeter × Apothem) / 2, the same relationship used for any regular polygon, since it can be split into n identical isosceles triangles - for the hexagon, that's (24 × 3.46) / 2 ≈ 41.57.
How do I find the area of a regular polygon?
First find the apothem, then use Area = (Perimeter × Apothem) / 2. For a hexagon with side 4: perimeter 24, apothem ≈ 3.46, area ≈ 41.57.
What is an apothem?
The apothem is the perpendicular distance from the center of a regular polygon to the midpoint of any side - it's always shorter than the distance from the center to a vertex.