Ctrl+k

Identify regular and irregular polygons

A regular polygon is a closed plane figure with at least three straight sides in which all side lengths and all interior angles are equal; a polygon is irregular if either side lengths or angle measures are not all equal. Classification depends on these invariant attributes, not on orientation, color, or apparent size, and supports later reasoning about symmetry, perimeter, angle relationships, and area.

Detailed Explanation: Identify regular and irregular polygons

A polygon is a closed shape made of at least three straight sides. To decide whether it is regular, check two things:

  1. Are all the side lengths equal?
  2. Are all the interior angles equal?
  • If both answers are yes, the polygon is regular.
  • If either answer is no, it is irregular.

The shape’s color, size, or direction does not matter.

Example: A pentagon has side lengths

4 cm, 4 cm, 4 cm, 4 cm, 4 cm4\text{ cm},\ 4\text{ cm},\ 4\text{ cm},\ 4\text{ cm},\ 4\text{ cm}

and each interior angle measures 108108^\circ.

Step 1: Check the sides.
All five sides are 44 cm, so the side lengths are equal.

Step 2: Check the angles.
All five angles measure 108108^\circ, so the angle measures are equal.

Step 3: Classify the polygon.
Both conditions are true, so the pentagon is a regular polygon.

If even one side had a different length or one angle had a different measure, the pentagon would be irregular.

Learn by doing: Identify regular and irregular polygons

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Classifying Polygons by Sides and Regular or Irregular


    ?