The diagonal line Formula for Squares, Rectangles, Cubes & Polygons

Polygons room the forms of our world. Computer and also television screens, doors, and sheets of record are all polygons. Diagonals of polygons are additionally useful. Learn how to instantly understand how numerous diagonals any type of polygon have the right to have by utilizing this formula:


Table that Contents

What"s a an easy Polygon?

A simple polygon is any two-dimensional (flat) form made just with straight sides that close in a space, and with political parties that carry out not overcome each other (if castle do, that is a complex polygon). A triangle is a polygon. A dart, kite, quadrilateral, and star room all polygons. Basic polygons have the right to be concave or convex. The formula us will use works because that all simple polygons.

You are watching: How to find diagonals in a polygon

What"s a Diagonal?

A diagonal of a polygon is a heat from a vertex come a non-adjacent vertex. Therefore a triangle, the most basic polygon, has actually no diagonals. Friend cannot draw a heat from one internal angle to any kind of other inner angle the is not likewise a side of the triangle. A quadrilateral, the next-simplest, has actually two diagonals. A pentagon, whether constant or irregular, has 5 diagonals.

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In convex, simple polygons, diagonals will certainly always be within the interior. Take into consideration a rectangle-shaped door. You can run a line from the peak hinge corner to the bottom, the contrary corner. You can also run a heat from the bottom hinge edge up to the top, opposite corner. Those space the only two diagonals possible.

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

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Diagonals in genuine Life

Diagonals in squares and also rectangles add strength to construction, whether for a home wall, bridge, or high building. You may see diagonal line wires provided to keep bridges steady. When residences are gift built, look because that diagonal braces that hold the wall surfaces straight and also true.

Bookshelves and scaffolding are braced with diagonals. Because that a catcher in soft ball or baseball come throw the end a runner at second base, the catcher throws follow me a diagonal from home plate to second.

The call or computer system screen you are viewing this class on is measured along its diagonal. A 21" screen never tells you the width and also height; it is 21" native one edge to an the opposite corner.


Diagonal that a Polygon Formula

To uncover all possible diagonals of a basic polygon with simply a couple of sides, girlfriend can easily count them. When the polygon it s okay a little complicated, count them have the right to be an extremely hard.

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Fortunately, basic formula exists to call you exactly how many diagonals a polygon has. Mental that any vertex (corner) is associated by political parties to two various other vertices, therefore those relations cannot count as diagonals. That vertex cannot affix to itself, either. So for n sides, us will instantly reduce the possible number of diagonals by three.

We also do not want to counting the exact same diagonal twice. Our door, for example, only has two diagonals; you carry out not counting going from the top hinge come bottom the contrary and earlier again. Girlfriend will need to divide any kind of answer through two.

Diagonal Formula

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


How To discover The diagonal of a Rectangle

Test this formula through something us know: diagonals the a rectangle. A rectangle has four sides and also 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):

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= 5(5 - 3)2

= 5(2)2

= 102

= 5

A pentagon has only five diagonals; our formula works.

Be really skeptical! shot it for a tetracontakaiheptagon, i beg your pardon is a ridiculously long (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 specifically how many diagonals have the right to be built inside (or outside) that any straightforward polygon, whether the form is convex or concave.

Diagonal of a Rectangle Formula

For rectangles, l is the length of the rectangle, and also b is the elevation of the rectangle.

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Lesson Summary

You have actually learned a lot about an especially important components of polygons, their diagonals. You now know how to determine the diagonals of any polygon, what part real-life examples of diagonals are, and also how to usage the formula, # of Diagonals = n(n - 3)2, where n is the variety of sides (or vertices) the the polygon. Also, us briefly spanned diagonal forumals to uncover the size of a diagonal in cubes squares, and also rectangles.

Next Lesson:

How to find the Perimeter that a Polygon


What friend learned:

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

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