The diagonal line Formula because that Squares, Rectangles, Cubes & Polygons

Polygons space the forms of our world. Computer and television screens, doors, and also sheets of record are all polygons. Diagonals of polygon are likewise useful. Learn how to instantly understand how many diagonals any type of polygon deserve to have by using this formula:

Table that Contents

What"s a an easy Polygon?

A simple polygon is any type of two-dimensional (flat) shape made just with directly sides that close in a space, and also with sides that carry out not cross each various other (if castle do, that is a facility polygon). A triangle is a polygon. A dart, kite, quadrilateral, and star room all polygons. Basic polygons deserve to be concave or convex. The formula we will use works for all simple polygons.

You are watching: Formula for diagonals of a polygon

What"s a Diagonal?

A diagonal of a polygon is a heat from a vertex to a non-adjacent vertex. So a triangle, the most basic polygon, has no diagonals. Girlfriend cannot attract a line from one inner angle to any type of other internal angle that is not additionally a next of the triangle. A quadrilateral, the next-simplest, has actually two diagonals. A pentagon, whether continuous or irregular, has 5 diagonals.


In convex, simple polygons, diagonals will always be within the interior. Consider a rectangle-shaped door. You deserve to run a line from the height hinge corner to the bottom, opposite corner. Friend can also run a heat from the bottom hinge edge up to the top, opposite corner. Those are the only two diagonals possible.

In concave, straightforward polygons, the diagonals may go outside the polygon, cross sides and partly lying in the shape"s exterior. They room still diagonals. Darts and also stars are typical examples of concave polygons v diagonals outside their shapes.


Diagonals in actual Life

Diagonals in squares and rectangles add strength come construction, whether because that a home wall, bridge, or high building. You might see diagonal wires offered to keep bridges steady. When dwellings are being built, look for diagonal braces that host the walls straight and true.

Bookshelves and scaffolding are braced through diagonals. For a catcher in softball or baseball to throw the end a runner at 2nd base, the catcher throws along a diagonal from residence plate come second.

The phone or computer screen you room viewing this class on is measured follow me its diagonal. A 21" screen never speak you the width and height; it is 21" from one corner to an the opposite corner.

Diagonal the a Polygon Formula

To discover all feasible diagonals the a simple polygon with simply a couple of sides, you can quickly count them. As soon as the polygon it s okay a little bit complicated, counting them have the right to be an extremely hard.


Fortunately, basic formula exist to tell you exactly how countless diagonals a polygon has. Mental that any vertex (corner) is connected by political parties to two various other vertices, for this reason those relations cannot count together diagonals. The vertex cannot affix to itself, either. So because that n sides, we will immediately reduce the possible variety of diagonals through three.

We likewise do not desire to counting the very same diagonal twice. Our door, for example, only has actually two diagonals; you carry out not count going native the peak hinge come bottom opposite and back again. Friend will have to divide any kind of answer through two.

Diagonal Formula

This leaves us with an elegant formula, whereby n is the variety of sides (or vertices):

How To find The diagonal line of a Rectangle

Test this formula v something we know: diagonals that a rectangle. A rectangle has 4 sides and four vertices.

# of Diagonals = n(n - 3)2

= 4(4 - 3)2

= 4(1)2

= 42

= 2

Be skeptical! shot it for a pentagon (five sides):


= 5(5 - 3)2

= 5(2)2

= 102

= 5

A pentagon has only 5 diagonals; ours formula works.

Be really skeptical! shot it because that a tetracontakaiheptagon, i m sorry is a ridiculously lengthy (but correct) name for a 47-gon:

= 47(47 - 3)2

= 47(44)2

= 2,0682

= 1,034

Trust the formula. A 47-gon has 1,034 diagonals. This formula works every time come tell you exactly how plenty of diagonals can be built inside (or outside) the any basic polygon, even if it is the shape is convex or concave.

Diagonal that a Rectangle Formula

For rectangles, l is the size of the rectangle, and also b is the height of the rectangle.

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Lesson Summary

You have learned a lot about specifically important components of polygons, their diagonals. You now know just how to recognize the diagonals of any polygon, what part real-life examples of diagonals are, and how to usage the formula, # of Diagonals = n(n - 3)2, wherein n is the number of sides (or vertices) of the polygon. Also, we briefly spanned diagonal forumals to find the length of a diagonal line in cubes squares, and also rectangles.

Next Lesson:

How to discover the Perimeter the a Polygon

What friend learned:

Once friend go with the reading and multimedia of this lesson, friend will learn to:

Identify diagonals of any straightforward polygonCite real-life instances of diagonalsRecall and use the formula for calculating the number of diagonals the a simple polygonDiscover the formulas because that calculating the length of diagonals the squares, rectangles, cubes & polygons