This drawing shows the train track joining the Train Yard to all the stations labelled from A to S. Find a way for a train to call at all the stations and return to the Train Yard. A pentagon has five diagonals lines drawn between the corners. You can trace over all of the diagonals without lifting your pencil and without going over any more than once.
Try it. Main menu Search. Hide Menu. Redblue Investigate the number of paths you can take from one vertex to another in these 3D shapes. Can the same thing be done with a hexagon 6 sides or with a heptagon 7 sides? This article has been viewed , times. Finding diagonals in a polygon is a necessary skill to develop in math. It may seem difficult at first, but is pretty simple once you learn the basic formula.
Using a very simple formula, you can calculate the number of diagonals in any polygon, whether it has 4 sides or 4, sides. To find out how many diagonals a polygon has, first count the number of sides, or straight lines, that make up the polygon. Then, subtract 3 from the number of sides. Next, multiply that number by the number of sides. For an alternate way to determine the number of diagonals in a polygon, read on! Did this summary help you? Yes No. Log in Social login does not work in incognito and private browsers.
Please log in with your username or email to continue. No account yet? Create an account. Edit this Article. We use cookies to make wikiHow great. By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article methods. Related Articles. Article Summary. Method 1. Know the names of polygons. You may need to first identify how many sides are present in the polygon. Each polygon has a prefix that indicates the number of sides it has.
Draw the polygon. If you wanted to know how many diagonals were present in a square, you would start by drawing the square. The easiest way to find diagonals and count them is to draw the polygon symmetrically, each side has the same length. For example, a stop sign is an octagon. Draw the diagonals. A diagonal is a line segment drawn from one corner of the shape to another, excluding the sides of the polygon. For a square, draw one line from the bottom left corner to the top right corner and another line from the bottom right corner to the top left corner.
Draw diagonals in different colors to make them easier to count. Note that this method gets much more difficult with polygons that have more than ten sides. Count the diagonals. There are two options for counting: you can count as you draw the diagonals or count them once they have been drawn. As you count each diagonal, draw a small number above the diagonal to denote that it has been counted. It is easy to lose track while counting when there are a lot of diagonals crossing each other.
For the square, there are two diagonals: one diagonal for every two vertices. A hexagon has 9 diagonals: there are three diagonals for every three vertices.
An octagon has 20 diagonals. Past the heptagon, it gets more difficult to count the diagonals because there are so many of them. Beware of counting a diagonal more than once. Take care when counting the diagonals to count each one only once. Each vertex has two diagonals, so if you counted each diagonal from every vertex twice, you might think there were 10 diagonals.
This is incorrect because you would have counted each diagonal twice! Practice with some examples. Draw some other polygons and count the number of diagonals. The polygon does not have to be symmetric for this method to work. In the case of a concave polygon, you may have to draw some of the diagonals outside the actual polygon.
A octagon has 20 diagonals. Method 2. Define the formula. You may see it either way, both equations are identical. This equation can be used to find the number of diagonals of any polygon. Note that the triangle is an exception to this rule.
Due to the shape of the triangle, it does not have any diagonals. Identify the number of sides in the polygon. To use this formula, you must identify the number of sides that the polygon has. The number of sides is given in the name of the polygon, you just need to know what each name means. Here are some of common prefixes you will see in polygons: [10] X Research source Tetra 4 , penta 5 , hexa 6 , hepta 7 , octa 8 , ennea 9 , deca 10 , hendeca 11 , dodeca 12 , trideca 13 , tetradeca 14 , pentadeca 15 , etc.
For example, a sided polygon would be written as gon. If you are given a picture of the polygon, you can simply count the number of sides. Plug the number of sides into the equation. Once you know how many sides the polygon has, you just need to plug that number into the equation and solve.
0コメント