2D Shapes
2D shapes have 2 dimensions - length and width.
We think of them as flat shapes as they have no height.
2D shapes can be created with straight or curvy lines.
They can be closed or open.
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Polygons
Polygons are special kinds of 2D shapes.
Poly is from Ancient Greek, meaning ‘many’ and gonia meaning ‘corner or angle’.
So a polygon has many angles.
Angles are created when the straight sides of a 2D shape meet at vertices (or corners).
An angle is the measure of turn between these two sides (see pic below).
A polygon is a closed shape. You need at least 3 sides to close a polygon.
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With all this mind, we can say that a polygon is a 2D shape with at least three sides and three angles.
Polygons are generally named by a Greek prefix that tells us the number of sides, followed by the suffix 'gon', with a few exceptions.
These prefixes are handy to know as they apply in other words we use to tell us 'how many', for example quadruplets (4 babies) or triatholon (3 events). Looking at the Latin, Greek and Arabic roots of mathematical words is a good way to promote transference of understanding.
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There are many common polygons we tend to know well: triangle (3 sides), rectangle (4 sides), square (4 sides - this is a special type of rectangle), pentagon (5 sides), hexagon (6 sides), and octagon (8 sides).
Ones we may not remember but are fascinating to know include: heptagon (7 sides), nonagon (9 sides), decagon (10 sides), hendecagon (11 sides), dodecagon (12 sides).
You can hear how dec - meaning 10, then relates to hendec (1 + 10) and dodec (2 + 10).
These sorts of patterns are fascinating.
Just for interest, a polygon with 100 sides called a hecatontagon! It is also called a hectagon which is a lot easier to say.
Quadrilaterals
Speaking of relationships, let’s have a look at some quadrilaterals.
These are special kinds of polygons.
They all have four (quad) sides (lateral) and therefore four angles but they don't (necessarily) look the same or have the same properties.
Regular and Irregular
Another interesting feature of polygons is that they can be regular or irregular.
This doesn’t mean it is something we see or don’t see often (or regularly), it has a special mathematical meaning.
A regular polygon has all sides the same length and all angles the same size.
