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`A = 1/2 * "n" * "r" ^2 * sin((2pi)/ "n" )`

Enter a value for all fields

This **Area of a Polygon (Outer Radius)** calculator computes the area of a regular polygon with (**n**) equal sides inside of an outer radius (**r**).

**INSTRUCTIONS:** Choose units and enter the following:

- (
**n**) - the number of sides of the regular polygon - (
**r**) - the outer radius of the polygon

**Total Area:** The area (**A**) is computed and returned in square meters. However, this can be automatically converted to other area units via the pull-down menu.

- Polygon Area from Number of Sides and Length of Sides
- Polygon Area from Number of Sides and Outer Radius
- Area of Polygon Segment from Number of Sides and Inner Radius
- Area of Polygon from Number of Sides and Inner Radius
- Length of the Sides of a Polygon based on the Outer Radius and Number of Sides
- Length of a Side of a Polygon from Inner Radius and Number of Sides
- Perimeter of a Polygon from Number of Sides and Length of Sides
- Polygon Perimeter from Outer Radius and Number of Sides
- Polygon Perimeter from Inner Radius and Number of Sides
- Polygon Perimeter from the Area and Number of Sides

The formula for the area of a polygon based on the number of sides and outer radius is:

A = ½• n • r² • sin( (2π) / n)

where:

- A is the area of a polygon
- r is the outer radius
- n is the number of sides

A regular **n**-sided polygon is a polygon with **n** equal length sides and is a polygon which has **n** equal angles at the **n** vertices of the polygon. Because of the symmetry of this construction, all the vertices of the regular polygon lie on the circle and the sides of the regular polygons form **n** chords of the circle.