Which polygon has no of sides diagonal

To unlock all 5, videos, start your free trial. A diagonal is a segment that connects two non-consecutive vertices in a polygon. The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides. To find the total number of diagonals in a polygon , multiply the number of diagonals per vertex n - 3 by the number of vertices, n, and divide by 2 otherwise each diagonal is counted twice. How many diagonals are a polygon with sides?

Well wouldn't make a whole lot of sense to draw a polygon with sides and draw on all those diagonals. There has to be a shortcut or a formula. Well, first let's back up. What is a diagonal? A diagonal is any line segment that connects two non-consecutive vertices. So if we look at a triangle. If I look at every single vertex, again the vertex is where two ends meet two sides meet.

There's no way for me to draw on a diagonal here because for this vertex both of these sides are consecutive. So there's no way for us to have any diagonals. If I look at a square however, I can see that there is one non-consecutive vertex if I look at this vertex. I look at another vertex there's only one non-consecutive vertex. So let's see if we can figure out the pattern. To do that, we're going to use this table over here where I have three columns; one for the number of vertices, one for the number of diagonals per vertex and the total number of diagonals that we see in a polygon.

So we've already started with two different polygons. We've talked about a triangle. A diagonal of a polygon can be defined as a line segment joining two vertices. From any given vertex, there are no diagonals to the vertex on either side of it, since that would lay on top of the side. Also, remember that there is obviously no diagonal from a vertex back to itself. This means there are three less diagonals than the number of vertices. We do not count diagonals to itself and one either side.

This is a diagonal definition. Here, we are going to discuss the number of diagonals in a polygon, diagonal definition. As described above, the number of diagonals from a single vertex is three less than the number of vertices or sides, or n There are a total number of N vertices, which gives us n n-3 diagonals.

But each diagonal of the polygon has two ends, so this would count each one twice. So as a final step we need to divide by 2, for the final formula:.

The diagonals of a polygon is a segment line in which the ends are non-adjacent vertices of a polygon. How many diagonals does n-polygon have? We can clearly see the triangle has no diagonals because each vertex has only adjacent vertices. For example, if a polygon has 54 diagonals, find how many sides it has. Notice there is a squared term.

This is a quadratic equation, so we can solve it either by factoring or using the quadratic formula. Here, we'll use factoring. But, since a polygon cannot have a negative number of sides, we know that this polygon must have 12 sides. In this problem it says if a polygon has 54 diagonals, how many sides does it have? So I guess you could even erase this in your mind and say how many vertices does it have?

Well we said that the number of diagonals is equal to the number of sides times the quantity of n minus 3 or the number of sides minus 3 all divided by 2. Well what are you given here? Now I see that I have a quadratic, if I want to solve I have to have 0 on one side of my equation. The easiest way is to solve by factoring. So if I can factor this into two binomials, I can use this zero product property to find my answers.