A polygon is a plane closed figure whose sides are straight lines. The term polygon (from the Greek poly for "many" and gwnos for "angle") sometimes
also refers to the interior of the polygon (the open area that this
path encloses) or to the union of both.
|Polygons are many-sided plane figures, the sides
and angles of which may be equal or unequal, giving symmetrical or
asymmetrical shapes. The simplest figure is the equilateral triangle
(A1) which has all sides and angles equal. The isosceles triangle
(A2) has two sides equal while (A3), which happens to be obtuse, has
sides of differing length. The simplest quadrilateral (B1) is the
square with equal sides and equal internal angles. The rectangle (B2)
has two pairs of equal and opposite sides with equal internal angles.
The parallelogram (B3) has two pairs of equal and opposite parallel
sides. The trapezium (B4) has only two parallel sides. The regular
pentagon (C) has five equal sides and the regular hexagon (D), six.
|The polygon ABCD is an irregular quadrilateral
with acute angles at A, C, and D and a
reentrant angle at B. AC and BD are its
A polygon is simple if it is described by a single, non-intersecting
boundary; otherwise it is said to be complex. A simple
polygon is called convex if it has no internal angles greater
than 180° otherwise it is called concave. A polygon
is called regular if all its sides are of equal length
and all its angles are equal. Any polygon, regular or irregular, has as
many angles as it has sides.
An n-gon is a polygon with n sides. For example, a hexagon is a 6-gon.
A self-intersecting polygon is a polygon with edges that cross other
= 180° - (360°/sides)
Formulae for regular polygons
In a regular n-sided polygon (see bottom diagram to the right), angle A = 180(1 - 2/n); angle O = 360/n; the area of the polygon = 1/2nld; and the radius r = d.sec(180/n).