Figure 1. 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.


Figure 2. 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 diagonals.

regular polygon

Figure 3. A regular polygon.

regular polygons

Figure 4. Regular polygons named.

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.


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 edges.


Regular polygons
name sides interior angle
= 180° - (360°/sides)
equilateral triangle 3 60
square 4 90
regular pentagon 5 108
regular hexagon 6 120
regular heptagon 7 128.57 (approx.)
regular octagon 8 135
regular nonagon 9 140
regular decagon 10 144
regular hectagon 100 176.4
regular megagon 106 179.99964
regular googolgon 10100 180 (approx.)


Formulae for regular polygons

In a regular n-sided polygon (see Figure 3), 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).