Idiot\'s Guides Basic Math and Pre-Algebra

192 Part 3: The Shape of the World

Polygons with More than Four Sides

Although triangles and quadrilaterals are the polygons you meet most often and the ones about

which you have the most information, there are others. The other polygons have more sides,

more vertices, more angles, and more diagonals, and there are a few rules they all follow. Even

those rules will depend on the number of sides, but once you know that, you can figure out some

things.

Remember that the name of a polygon is determined by how many sides it has. When there isn’t

a particular name for a polygon with that number of sides, you just tack –gon on to the number of

sides. A polygon with seventeen sides would be a seventeen-gon.

Naming Polygons by Sides

Sides^5678910

Name Pentagon Hexagon Heptagon Octagon Nonagon Decagon

Number of Diagonals

The more sides a polygon has, the more vertices it has, so the more diagonals you can draw.

A triangle with three vertices has no diagonals, but a quadrilateral with four vertices has two

diagonals. How many are there in a pentagon? Or a hexagon?

Let’s start with a pentagon, with five sides and five vertices. You can start a diagonal from any

one of the five vertices, but once you pick the starting point, you have four vertices left. Of those

four, you can only draw diagonals to two others. If you try to draw to the other two, you’ll be

tracing over a side. So you have five places to start, but you can’t end where you started, and you

can’t trace over a side, so you have only two places to end. You can draw two diagonals from that

vertex, and there are five vertices, so there are 10 diagonals in a pentagon, right?

A

B

C

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