A polygon is merely a level figured enclosed by straight lines. In Greek, poly means many and gon means angle. The simplest polygon is a triangle which has actually 3 sides and 3 angles which sum up come 180 degrees. Here, the diagonal line of a polygon formula is offered with description and solved examples.


There deserve to be numerous sided polygons and they can either be continual (equal length and interior angles) or irregular. A polygon can be additional classified together concave or convex based upon its interior angles. If the interior angles are less than 180 degrees, the polygon is convex, otherwise, that is a concave polygon. It have to be detailed the sides of a polygon are constantly a straight line.

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In a polygon, the diagonal line is the heat segment the joins two non-adjacent vertices. An exciting fact about the diagonals of a polygon is that in concave polygons, at least one diagonal line is actually exterior the polygon.


Now, because that an “n” sided-polygon, the variety of diagonals have the right to be derived by the adhering to formula:

Number the Diagonals = n(n-3)/2

This formula is simply created by the mix of diagonals the each vertex sends out to an additional vertex and also then individually the total sides. In various other words, one n-sided polygon has actually n-vertices which can be joined v each various other in nC2 ways.

Now by individually n v nC2 ways, the formula obtained is n(n-3)/2.

For example, in a hexagon, the complete sides room 6. So, the complete diagonals will certainly be 6(6-3)/2 = 9.


Example 1:

Find the total variety of diagonals included in one 11-sided regular polygon.


In an 11-sided polygon, full vertices room 11. Now, the 11 vertices can be joined with each various other by 11C2 means i.e. 55 ways.

Now, there are 55 diagonals feasible for an 11-sided polygon which consists of its sides also. So, subtracting the sides will give the full diagonals contained by the polygon.

So, total diagonals contained within an 11-sided polygon = 55 -11 i.e. 44.

Formula Method:

According come the formula, variety of diagonals = n (n-3)/ 2.

So, 11-sided polygon will contain 11(11-3)/2 = 44 diagonals.

Example 2:

In a 20-sided polygon, one vertex does not send any diagonals. Find out how plenty of diagonals does that 20-sided polygon contain.


In a 20-sided polygon, the complete diagonals room = 20(20-3)/2 = 170.

But, since one peak does not send any diagonals, the diagonals by the vertex demands to be subtracted indigenous the total number of diagonals.

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In a polygon, it is recognized that every vertex renders (n-3) diagonals. In this polygon, every vertex makes (20-3) = 17 diagonals.

Now, because 1 crest does no send any diagonal, the full diagonal in this polygon will be (170-17) = 153 diagonals.