A regular polygon is simply a polygon whose sides all have the same length and angles all have the same measure. The most well known regular polygons are the equilateral triangle and square, both pictured below.

Examples of Regular Polygons

Regular Triangle (a.k.a. Equilateral)

Regular Quadrilateral (a.k.a. square)

Regular Hexagon

Regular Pentagon

Non-Examples of Regular Polygons

Non-regular Triangle

Non-regular Quadrilateral

Non-regular Pentagon

Non-regular Hexagon

As you can see from the pictures above, the side lengths and interior angles are different sizes (ie have different measurements)