Diagonals of a polygon

But note that the excluded polygons might not be triangles, indeed might not be convex, so the line intersection test might be awkward. Can we figure out how many diagonals a polygon has? But because a polygon can’t have a negative number of sides, n must be 15. An interesting fact about the diagonals of a polygon is that in concave polygons, at least one diagonal is actually outside the polygon. A regular pentagon has five diagonals of equal length, each formed by a line going from one vertex of the pentagon to another. A regular polygon is a polygon all of whose sides are congruent and all of whose angles are congruent.



Then the diagonals you want are the diagonals of the original polygon that don't intersect any of the excluded polygons. In a regular hexagon, each angle = 720°/6 = 120° You know what the formula for the number of diagonals in a polygon is, and you know that the polygon has 90 diagonals, so plug 90 in for the answer and solve for n: Thus, n equals 15 or –12. But note that the excluded polygons might not be triangles, indeed might not be convex, so the line intersection test might be awkward. A polygon's diagonals are line segments from one corner to another (but not the edges). The number of diagonals of an n-sided polygon is: n(n − 3) / 2 Given n > 3, find number of diagonals in n sided convex polygon. So if we let diag(n) be the number of diagonals for a polygon with n sides, we get the formula: diag(n) = diag(n-1) + n - 3 + 1 or diag(n-1) + n - 2 The first formula is better, since it actually gives you the answer. Find a formula that tells how to determine the number of diagonals there are in any regular convex polygon with n sides. Now, for an “n” sided-polygon, the number of diagonals can be obtained by the following formula: Number of Diagonals = n(n-3)/2 You cannot draw a line from one interior angle to any other interior angle that is not also a side of the triangle. 439 2 2 silver badges 3 3 bronze badges.

Of course we can. So a triangle, the simplest polygon, has no diagonals.

A diagonal of a polygon is a line from a vertex to a non-adjacent vertex. A hexagon is any six-sided polygon, and the sum of its angles is 720°, as we saw above. answered Dec 8 '10 at 12:50. dmuir dmuir.

share | improve this answer. Use the below calculator to find out the total number of diagonals in a polygon, using the formula given below without drawing the shape and counting the diagonals. From that, we could find many other angles inside the shape. share … 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 … Diagonal is a straight line joining two vertices of polygon.


In a polygon, the diagonal is the line segment that joins two non-adjacent vertices. Diagonals of a Regular Hexagon.

So a triangle, the simplest polygon, has no diagonals. We could use analogous means to find angles involving the diagonals of any higher polygon. For any polygon, a “diagonal” is defined as a line segment that runs from one vertex of the polygon to another, and which runs through the interior of the polygon.

Because if you connect two adjacent vertices, that's just a side of the polygon, not a diagonal! Examples : Input : 5 Output : 5

Why do we specify non-adjacent? For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3). Polygon Diagonals The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides. According to Wikipedia, In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.Informally, any sloping line is called diagonal. We can see that for one of these diagonals, an isosceles triangle is formed where the two equal side lengths between the vertices joined by the diagonal are the other two sides. 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. Then the diagonals you want are the diagonals of the original polygon that don't intersect any of the excluded polygons. A diagonal is a line segment which connects two non-adjacent vertices of a polygon.


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