Polygon Area Calculator

Polygon Area is evaluated from Number of Sides and Side Length. The calculation reports Area, Perimeter and Interior Angle.

Results

Thanks — we’ve logged this for review.

About the Polygon Area Calculator

Polygon Area is treated here as a quantitative relation between Number of Sides and Side Length and Area, Perimeter, Interior Angle and Apothem.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
A = ns^2 / (4 x tan(pi/n))
Interior angle = (n - 2) x 180 deg / n
Apothem = s / (2 x tan(pi/n))

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

A = ns^2 / (4 x tan(pi/n))
Interior angle = (n - 2) x 180 deg / n
Apothem = s / (2 x tan(pi/n))

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Hexagonal Tile — Bathroom Floor

Inputs

n_sides: 6 side_len: 4
Area: 41.569219 sq units. Perimeter: 24 units. Interior Angle: 120 deg. Apothem: 3.464102 units. Number of Diagonals: 9

With Number of Sides = 6 and Side Length = 4 as the stated inputs, the result is Area = 41.569219 sq units, Perimeter = 24 units and Interior Angle = 120 deg. Each value corresponds to the declared output fields.

Example 2: Octagonal Stop Sign

Inputs

n_sides: 8 side_len: 12.5
Area: 754.441738 sq units. Perimeter: 100 units. Interior Angle: 135 deg. Apothem: 15.088835 units. Number of Diagonals: 20

With Number of Sides = 8 and Side Length = 12.5 as the stated inputs, the result is Area = 754.441738 sq units, Perimeter = 100 units and Interior Angle = 135 deg. Each value corresponds to the declared output fields.

Example 3: Pentagon — Home Plate

Inputs

n_sides: 5 side_len: 8.5
Area: 124.304492 sq units. Perimeter: 42.5 units. Interior Angle: 108 deg. Apothem: 5.849623 units. Number of Diagonals: 5

With Number of Sides = 5 and Side Length = 8.5 as the stated inputs, the result is Area = 124.304492 sq units, Perimeter = 42.5 units and Interior Angle = 108 deg. Each value corresponds to the declared output fields.

Example 4: Garden Gazebo — Decagonal Platform

Inputs

n_sides: 10 side_len: 6
Area: 276.991518 sq units. Perimeter: 60 units. Interior Angle: 144 deg. Apothem: 9.233051 units. Number of Diagonals: 35

With Number of Sides = 10 and Side Length = 6 as the stated inputs, the result is Area = 276.991518 sq units, Perimeter = 60 units and Interior Angle = 144 deg. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate area of a hexagonal tile or floor section
  • Find area of a pentagon-shaped room
  • Determine regular polygon dimensions for design
  • Compute area of land parcel from coordinates