Perimeter of a Polygon Calculator
Calculate polygon perimeter using side lengths, coordinates, or regular polygon properties
Calculate Polygon Perimeter
Must be 3 or more for a valid polygon
Length of each side (all sides are equal in regular polygons)
Calculation Results
Formula used: Perimeter = n × a = 6 × 0
Input Validation
Example Calculations
Regular Octagon
Given: 8 sides, each side = 5 cm
Formula: Perimeter = n × a
Calculation: Perimeter = 8 × 5 = 40 cm
Irregular Quadrilateral
Given: Sides = 3, 4, 5, 6 units
Formula: Perimeter = Σ aᵢ
Calculation: Perimeter = 3 + 4 + 5 + 6 = 18 units
Triangle from Coordinates
Vertices: (0,0), (3,0), (1.5,2.6)
Side 1: √[(3-0)² + (0-0)²] = 3
Side 2: √[(1.5-3)² + (2.6-0)²] = 3
Side 3: √[(0-1.5)² + (0-2.6)²] = 3
Perimeter: 3 + 3 + 3 = 9 units
Common Polygons
Perimeter Formulas
Regular Polygon
P = n × a
n = sides, a = side length
Irregular Polygon
P = Σ aᵢ
Sum of all side lengths
From Coordinates
P = Σ √[(xᵢ₊₁-xᵢ)² + (yᵢ₊₁-yᵢ)²]
Distance formula
Calculation Tips
Regular polygons have all sides equal
Minimum 3 sides to form a polygon
Coordinates method works for any polygon
Perimeter is always the sum of all sides
Understanding Polygon Perimeter Calculation
What is a Polygon?
A polygon is a closed two-dimensional shape made up of straight line segments. The perimeter is the total distance around the polygon's boundary. Common polygons include triangles (3 sides), squares (4 sides), pentagons (5 sides), and hexagons (6 sides).
Types of Polygons
- •Regular: All sides and angles are equal
- •Irregular: Sides and/or angles are different
- •Convex: All interior angles less than 180°
- •Concave: At least one interior angle greater than 180°
Calculation Methods
Regular Polygon
Simplest method - multiply sides by length
P = n × a
Irregular Polygon
Sum all individual side lengths
P = a₁ + a₂ + ... + aₙ
Coordinate Method
Calculate distances between vertices
P = Σ √[(x₂-x₁)² + (y₂-y₁)²]
Note: The coordinate method is most versatile and works for any polygon shape, including irregular and concave polygons.