Irregular — Definition, Formula & Examples
Irregular means a shape does not have all sides equal in length and all angles equal in measure. An irregular polygon has sides or angles that differ from one another.
A polygon is classified as irregular if it is not equilateral, not equiangular, or neither — that is, at least one side differs in length from another side, or at least one interior angle differs in measure from another interior angle.
How It Works
To decide if a polygon is irregular, check two things: the lengths of all its sides and the measures of all its angles. If every side is the same length and every angle is the same measure, the shape is regular. If even one side or one angle is different, the shape is irregular. Most polygons you see in everyday life — like a rectangular door or a triangular road sign — are irregular.
Example
Problem: A quadrilateral has sides measuring 3 cm, 5 cm, 3 cm, and 5 cm, with angles of 80°, 100°, 80°, and 100°. Is it regular or irregular?
Check the sides: The sides are 3, 5, 3, and 5. They are not all the same length.
Conclusion: Since the sides are not all equal, the quadrilateral is irregular. (The angles are also not all equal, which confirms it.)
Answer: The quadrilateral is irregular.
Why It Matters
Recognizing whether a polygon is regular or irregular tells you which formulas you can use. For regular polygons, you can use shortcuts involving the apothem or a single side length. For irregular polygons, you often need to measure each side and angle individually to find perimeter or area.
Common Mistakes
Mistake: Thinking a shape is regular just because all sides are equal, even though the angles differ.
Correction: A regular polygon requires both all sides equal and all angles equal. A rhombus, for example, has four equal sides but its angles can differ, making it irregular.