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 Calculators
- 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 Math / Science
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.