A polygon is a closed planar shape with straight sides.
That is, if you join several lines together end-to-end to make a closed shape, what you
have is called a polygon.
If one of the sides is curved, then it’s not a polygon.
All the sides of a polygon are straight lines.
If the shape isn’t closed, it’s also not a polygon.
Some people say this is actually a simple polygon, when none of the lines cross each
other.
If you allow lines that cross over, you have a complex polygon.
Personally I don’t.
To me, this is not a complex polygon, it’s two polygons joined at one vertex.
We classify polygons by counting the number of sides, and describing it as either convex
or concave, and regular or irregular.
A polygon is regular if all the sides are the same length and all the angles are equal.
It’s called concave if at least one of the vertices makes an internal reflex angle; it
sticks into the shape.
Otherwise it’s called convex.
In fact, if it’s regular, it has to be convex; you can’t have a regular concave polygon.
So you only really need to say one of these words, regular, convex or concave.
The names for the number of sides are derived mostly from Greek, with some from Latin.
A three-sided polygon is a triangle (literally “three angles”, tri-angle), and a four-sided
polygon is a quadrilateral (which means “four sides”).
We have special names for different kinds of triangles and quadrilaterals, because we
use them so often.
How many of the others do you know?
A five-sided polygon is a pentagon.
Six sides is a hexagon.
Seven is a heptagon; some people call it a septagon instead, which is Latin instead of
the Greek heptagon.
Eight is an octagon.
Nine we usually call a nonagon, which is actually a Latin name; the Greek is enneagon.
Ten is a decagon.
Names beyond ten are not as commonly heard.
However two are worth knowing.
A twelve-sided polygon is a dodecagon; that’s the shape of an Australian fifty-cent piece.
And a polygon with twenty sides is called an icosagon.
Let me show you some examples.
This polygon has five sides.
It’s convex because there are no vertices pointing into the inside of the shape.
And the side lengths and angles are not all the same.
That makes it an irregular convex pentagon.
This one has six sides, and it’s also irregular.
But one of these vertices points into the centre of the shape.
The internal angle at this vertex is greater than a hundred and eighty degrees: it’s
a reflex angle.
So this shape is concave.
It’s an irregular concave hexagon.
In fact you can just call it a concave hexagon, because concave polygons are always irregular.
How many sides does this polygon have?
All the sides and angles are equal, and the vertices all point outwards.
With ten sides, that makes it a regular convex decagon, or just a regular decagon, since
regular polygons are always convex.
This one is a triangle.
The sides are all different, and it’s impossible to have a concave triangle, so that means
it’s an irregular triangle.
Actually, we usually call an irregular triangle a scalene triangle.
There are special names for classifying triangles.
Here’s another concave shape.
See how some of the vertices point inwards?
See the internal reflex angles?
How many sides does it have?
Eleven!
It’s an irregular concave henagon.
(Don’t worry, I didn’t actually tell you what an eleven-sided polygon was called.)
This shape is also concave and irregular.
Can you see the internal reflex angles?
How many sides does it have?
Twelve.
It’s an irregular concave dodecagon.
Finally, here’s a four-sided shape, a quadrilateral.
It’s convex, but not regular.
So it’s an irregular convex quadrilateral.
Actually, this shape is called a trapezium.
There are special names for classifying quadrilaterals.