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

Polygons space the forms of our world. Computer and also television screens, doors, and sheets of file are every polygons. Diagonals of polygon are likewise useful. Learn exactly how to instantly recognize how many diagonals any type of polygon have the right to have by making use of this formula:

### Table the Contents

## What"s a basic Polygon?

A **simple polygon** is any kind of two-dimensional (flat) form made just with straight sides that close in a space, and with political parties that do not overcome each other (if castle do, the is a complex polygon). A triangle is a polygon. A dart, kite, quadrilateral, and also star are all polygons. Straightforward polygons deserve to be concave or convex. The formula we will usage works because that *all* straightforward polygons.

You are watching: How many diagonals does a quadrilateral have

## What"s a Diagonal?

A **diagonal** that a polygon is a line from a vertex to a non-adjacent vertex. So a triangle, the simplest polygon, has no diagonals. Friend cannot draw a heat from one inner angle to any other inner angle the is not likewise a next of the triangle. A quadrilateral, the next-simplest, has two diagonals. A pentagon, whether consistent or irregular, has five diagonals.

**In convex, simple polygons, diagonals will certainly always be within the interior**. Think about a rectangular door. You have the right to run a line from the top hinge edge to the bottom, the contrary corner. Girlfriend can likewise run a line from the bottom hinge edge up come the top, the contrary corner. Those space the only two diagonals possible.

In **concave, simple polygons, the diagonals may go exterior the polygon**, crossing sides and partly lie in the shape"s exterior. They are still diagonals. Darts and stars are common examples of concave polygons through diagonals external their shapes.

### Diagonals in real Life

Diagonals in squares and also rectangles include strength come construction, whether for a home wall, bridge, or tall building. You may see diagonal wires used to keep bridges steady. When dwellings are being built, look because that diagonal braces that hold the walls straight and true.

Bookshelves and also scaffolding are braced with diagonals. Because that a catcher in soft ball or baseball to throw the end a runner at 2nd base, the catcher throws along a diagonal line from residence plate to second.

The phone or computer screen you space viewing this class on is measured follow me its diagonal. A 21" screen never speak you the width and also height; that is 21" native one corner to an the contrary corner.

## Diagonal that a Polygon Formula

To discover all possible diagonals of a simple polygon with just a few sides, you can conveniently count them. When the polygon gets a little complicated, count them deserve to be really hard.

Fortunately, basic formula exists to call you precisely how plenty of diagonals a polygon has. Psychic that any kind of vertex (corner) is linked by sides to two various other vertices, so those relationships cannot count together diagonals. The vertex cannot affix to itself, either. So because that n sides, we will automatically reduce the possible number of diagonals by three.

We likewise do not desire to counting the very same diagonal twice. Our door, for example, only has two diagonals; you do not counting going from the height hinge come bottom the opposite and earlier again. Friend will need to divide any kind of answer through two.

### Diagonal Formula

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

## How To uncover The diagonal line of a Rectangle

Test this formula with something us know: diagonals the 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! try it because that a pentagon (five sides):

= 5(5 - 3)2

= 5(2)2

= 102

= 5

A pentagon has actually only 5 diagonals; our 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 functions every time to tell you exactly how countless diagonals can be constructed inside (or outside) the any basic polygon, whether the shape is convex or concave.

### Diagonal that a Rectangle Formula

For rectangles, together is the length of the rectangle, and b is the height of the rectangle.

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## Lesson Summary

You have learned a lot of about specifically important components of polygons, their diagonals. You currently know exactly 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 variety of sides (or vertices) that the polygon. Also, we briefly extended diagonal forumals to uncover the length of a diagonal line in cubes squares, and rectangles.

### Next Lesson:

How to uncover the Perimeter of a Polygon

## What you learned:

Once you go through the reading and also multimedia the this lesson, friend will find out to:

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