How to find no of diagonals in a polygon

Diagonals of a polygon are the lines that connect the alternate vertices of the polygon. A polygon is a closed figure with n sides where n is always greater than equal to 3. A polygon is a closed shape with three or more straight sides, and diagonals are the line segments that connect any two non-adjacent vertices of the polygon. Polygon can be defined as a closed figure which is formed by joining the straight lines.

The number of diagonals and their attributes vary depending on the type of polygon and the number of sides. Let's review what a polygon is and what a diagonal is before learning the diagonal of a polygon formula. A closed shape made up of three or more line segments is called a polygon. A line segment generated by joining any two non-adjacent vertices forms the diagonal of a polygon. Let's look at the formula for a polygon's diagonal, as well as some examples of solved problems. You can quickly count all of the possible diagonals of a basic polygon with a few sides. Counting polygons can be difficult when they become more intricate.

How to find no of diagonals in a polygon

A polygon is simply a plain figured enclosed by straight lines. In Greek, poly means many and gon means angle. The simplest polygon is a triangle which has 3 sides and 3 angles which sum up to degrees. Here, the diagonal of a polygon formula is given with description and solved examples. There can be numerous sided polygons and they can either be regular equal length and interior angles or irregular. A polygon can be further classified as concave or convex based on its interior angles. If the interior angles are less than degrees, the polygon is convex , otherwise, it is a concave polygon. It should be noted the sides of a polygon are always a straight line. In a polygon, the diagonal is the line segment that joins two non-adjacent vertices. An interesting fact about the diagonals of a polygon is that in concave polygons, at least one diagonal is actually outside the polygon.

In other words, an n-sided polygon has n-vertices which can be joined with each other in nC2 ways. Once you know how many sides the polygon has, you just need to plug that number into the equation and solve. Diagonal of a Polygon Formula.

Last Updated: March 7, Fact Checked. This article was co-authored by Jake Adams. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed , times.

Home » Geometry » Polygon » Diagonals of a Polygon. The diagonal of a polygon is the line segment that links the opposite, nonadjacent corners or vertices of that polygon. For an n -sided regular polygon, the number of diagonals can be obtained using the formula given below:. This equation is obtained by adding the number of diagonals that each vertex sends to another vertex and then subtracting the total number of sides from it. For example, in a pentagon the total number of sides is five. Find the number of diagonals in a sided regular polygon. In a sided polygon, one vertex does not have any diagonals. Calculate how many diagonals the sided polygon contains.

How to find no of diagonals in a polygon

Last Updated: March 7, Fact Checked. This article was co-authored by Jake Adams. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. 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.

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Problem 7: How many diagonals does a polygon have if the sides are 40? An octagon has 20 diagonals. You can quickly count all of the possible diagonals of a basic polygon with a few sides. Method 1. But there are only 5 diagonals. This article is being improved by another user right now. Categories: Geometry Mathematics. Submit a Tip All tip submissions are carefully reviewed before being published. Not Helpful 0 Helpful 6. Great help explaining the topic to children.

A diagonal is a slant line or a sloping line that connects two vertices of a polygon, and those vertices should not be on the same edge.

It has 2 diagonals. Note that this method gets much more difficult with polygons that have more than ten sides. Diagonal of a Polygon Formula. Trending Articles How to. Create an account. Share yours! If you are given a picture of the polygon, you can simply count the number of sides. We can clearly see the triangle has no diagonals because each vertex has only adjacent vertices. Add Other Experiences. So as a final step we need to divide by 2, for the final formula:. Open In App. Did this summary help you? You Might Also Like How to. Not Helpful 7 Helpful