Regular and irregular polygons
Maths · Key Stage 2 · The School
What makes a polygon regular
A polygon is any flat shape with straight sides. A REGULAR polygon has all its sides the same length, and all its angles the same size too. Both things have to be true together. A shape with equal sides but unequal angles does not count as regular. Neither does a shape with equal angles but unequal sides. Both checks must pass for the shape to earn the word "regular".
Naming polygons by their sides
A polygon with 5 sides is a pentagon. One with 6 sides is a hexagon. One with 8 sides is an octagon. The name always comes from the number of sides, using a pattern borrowed from Greek number words. Learning a few names makes the rest easier to guess. A polygon with 7 sides, for instance, is a heptagon, following the very same pattern.
Why a rectangle fails the test
A rectangle has four equal angles, all right angles. But its sides are not all equal — two are long, and two are short. Because the sides fail the test, a rectangle is an irregular polygon, even though its angles alone would pass. Both parts of the test have to hold.
Checking a real shape
A road sign is a shape with 8 sides. Measure each side: they are all exactly the same length. Measure each angle: they are all exactly the same size too. Both tests pass, so the sign is a regular octagon. If even one side or angle had been different, the shape would count as irregular instead.