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:
Total Area (A): The area returned in square meters. However, this can be automatically converted to other area units via the pull-down menu.
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)
A regular polygon is a geometric shape with three or more straight sides where every side is the same length and every angle between connecting sides are the same angle. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length . Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side. As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form n isosceles triangles of equal area.
The names of polygons vary based on the number of sides as follows:
Polygon Area Calculators:
Polygon Side Calculators
Polygon Perimeter Calculators
Other Polygon Calculators