Irregular Polygon Definition

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An irregular polygon can be defined as a polygon having the length of all its sides not equal to each other. In

an irregular polygon the interior angles are not equal to each other. Irregular polygons can be categorized

into following two types:

Convex irregular polygon: They have all their interior angles less than 180 degree.

Concave irregular polygon: They can have some of their interior angles greater than 180 degree.

Example 1: Identify if the polygon given in the options below irregular or not and give reasons for your

a)    Polygon ABCDEF with AB = 6 cm, BC = 6 cm, CD = 7 cm, DE = 5 cm, EF = 5 cm, FA = 7 cm.

b)    Polygon PQRST with angle P = 75 degree, angle Q = 75 degree, angle R = 75 degree, angle S = 75

degree, angle T = 75 degree.

Solution:  a) Since the length of all the side of the given polygon are not equal, so this polygon is irregular

polygon.

Example 2: Write whether the polygon given below is a convex irregular polygon or concave irregular

Polygon DEFGH with angle D = 160 degree, angle E = 85 degree, angle F = 90 degree, angle G = 205

degree, angle H = 110 degree.

Solution: The given polygon is a concave irregular polygon. In a concave irregular polygon at least one

interior angle is greater than 180 degree. Here angle G is greater than 180 degree. Thus the given polygon

can be classified as a concave irregular polygon.