How to Find the Number of Diagonals in a Polygon

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  • 0:07 Polygons
  • 0:39 Diagonals
  • 2:11 The Formula
  • 4:19 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

At first, you might think that the diagonals of a polygon are pretty useless, but watch this video lesson to learn how diagonals are used in real life. You will learn the formula to find how many diagonals a polygon has as well as how to use it.


Polygons are everywhere! Look around, and you will see that most man-made structures are based on polygon shapes. What shape are office buildings? What shape are windows and doors? What about stop signs? All of these are polygons. We can define a polygon as a flat shape with straight sides. Triangles, rectangles, pentagons, and hexagons are all examples of polygons. As long as the shape is surrounded by straight sides, we can call it a polygon.


Every polygon has a number of diagonals except for the triangle. A diagonal is a line that connects two non-adjacent corners together. If you had a rectangle, for example, you would be able to draw two diagonals through it. You should start at one point and look for all the points that are not next to that point. The point next to your point is already connected by a side of the polygon. You can think of it as a game of 'connect all the corners.' For the rectangle, only two diagonals are needed to connect all the corners to each other. Try it out for yourself. For a pentagon, a polygon with five sides, you will see that five diagonals are needed to connect all the corners.

In the real world, diagonals are quite useful. Most likely, you are watching this video lesson on a computer screen. Computer screens are labeled based on their diagonal. So, a 17-inch computer monitor tells you that the diagonal measures 17 inches across. This measurement is only for the screen part and not the molding around it. Measure your own computer screen's diagonal to find out how large it is considered. Also, in some cities, a diagonal crosswalk is used for pedestrians who need to cross in that direction. It makes it easier for them so they don't have to first cross one street and then wait to cross the next street. Of course, all the lights are red at these intersections as pedestrians make their way to their desired corner.

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