Area of a Polygon

Area of a Regular Polygon

            The number of square units it takes to completely fill a regular polygon. Four different ways to calculate the area are given, with a formula for each.

1. Given the length of a side.

By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the area is given by the formula:

Area =          s2 N                   A tan(180/N)

where S  is the length of any side N  is the number of sides TAN  is the tangent function calculated in degrees

2. Given the radius (circumradius)

If you know the radius (distance from the center to a vertex, see figure above):

Area=R2Nsin(360/N)                       2

where             R  is the radius (circumradius)           N  is the number of sides             SIN  is the sine function calculated in degrees

3. Given the apothem (inradius)

If you know the apothem, or inradius, (the perpendicular distance from center to a side. See figure above)

Area = A2Ntan (180/N)

where A is the length of the apothem (inradius) N  is the number of sides TAN  is the tangent function calculated in degrees .

4. Given the apothem and length of a side

If you know the apothem (the perpendicular distance from center to a side. See figure above) and the length of a side, first determine the perimeter by mutiplying the side length by N. The area is given by

Area = AP

            2

where A is the length of the apothem P  is the perimeter