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Q: How many heptagons can be drawn by joining the vertices of a polygon with 10 sides?

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10c5

This is a diagonal line. The definition of a diagonal is a line that joins two nonconsecutive vertices or corners of a polygon.

5 diagonals * * * * * That is not correct since two of these would be lines joining the vertex to adjacent vertices (one on either side). These are sides of the polygon, not diagonals. The number of diagonals from any vertex of a polygon with n sides is n-3.

10 ... any polygon it is 2 less than the number of sides or vertices wince they are the same.

N-2 according to yahoo answers

A line connecting to non-adjacent vertices of a polygon is called a diagonal of the polygon. A triangle has no diagonals since each vertex is adjacent to the next. A quadrilateral has two diagonals.

n-3 diagonals. Of the n vertices of the polygon, you cannot draw diagonals to the two adjacent vertices since these are sides of the polygon and so not diagonals. And you cannot draw a diagonal from a vertex to itself. So those are three vertices that are ruled out, leaving n-3.

Suppose a polygon has n vertices (and sides). From each vertex, a diagonal can be drawn to all vertices, excluding itself and the two adjacent vertices. So n-3 diagonals can be drawn from each vertex. Multiplying by the full complement of n vertices gives n(n-3). However, as things stand we have counted each diagonal twice: once at both ends. Dividing by two gives the actual number of diagonals. number of diagonals = n(n-3)/2

It consists of 98 triangles and has 4850 diagonals

In a Frequency Polygon, a line graph is drawn by joining all the midpoints of the top of the bars of a histogram. A frequency polygon gives the idea about the shape of the data distribution. The two end points of a frequency polygon always lie on the x-axis.

An apothem is a line drawn perpendicular to a side of a regular polygon from the center of the polygon. A polygon is not a circle so it cannot have a radius. The radius of a circle is drawn from the center to any point in the circumference of the circle. You can draw a circle which encloses the regular polygon touching all vertices. The polygon is said to be inscribed in the circle. The apothem will be less than the radius because the radius is not perpendicular to any side, it can be drawn to a vertex but the apothem is perpendicular to a side, so it is shorter. Ex: draw a square with a circle which inscribes it. You can see that the apothem will be less than the radius.

Suppose a polygon has n vertices (and sides).From each vertex, a diagonal can be drawn to all vertices, excluding itself and the two adjacent vertices. So n-3 diagonals can be drawn from each vertex.Multiplying by the full complement of n vertices gives n(n-3). However, as things stand we have counted each diagonal twice: once at both ends. Dividing by two gives the actual number of diagonals.number of diagonals = n(n-3)/2

1. A histogram is two-dimensional while a polygon has more than four dimensions. 2. A histogram may be drawn from a histogram by joining the mid points of upper horizontal sides of each rectangle. But a histogram can not be drawn from a polygon. 3. The frequency polygon of several distributions can be plotted on the same axis while more than one histogram can not be drawn on the same axis. 4. It is possible to compare the polygon of several distributions as they can be plotted on the same axis. But to compare histogram we must have a graph for each distribution. 5. Polygon an outline of data pattern is sketched more clearly than histogram.

A dodecagon is a regular polygon that can be drawn using rotations. These are normally drawn in a Geometer's Sketchpad.

One AnswerFor quadrilaterals (parallelogram, rectangle, rhombus, trapezoid) its called a diagonal Another:For any polygon or polyhedron, it is a diagonal.

A diagonal of a polygon is a segment drawn from one vertex to another non-adjacent vertex in a polygon. This leaves 32 diagonals that can be drawn from one vertex in a 35 sided polygon.

47 sides. Take a vertex of an n-sided polygon. There are n-1 other vertices. It is already joined to its 2 neighbours, leaving n-3 other vertices not connected to it. Thus n-3 diagonals can be drawn in from each vertex. For n=50, n-3 = 50-3 = 47 diagonals can be drawn from each vertex. The total number of diagonals in an n-sided polygon would imply n-3 diagonals from each of the n vertices giving n(n-3). However, the diagonal from vertex A to C would be counted twice, once for vertex A and again for vertex C, thus there are half this number of diagonals, namely: number of diagonals in an n-sided polygon = n(n-3)/2.

circumscribed means the polygon is drawn around a circle, and inscribed means the polygon is drawn inside the circle. See related links below for polygon circumscribed about a circle and polygon inscribed in a circle.

38 diagonals

By drawing all the diagonals from one vertex, the polygon is divided up into triangles. The sum of the interior angles of the polygon is equal to the sum of the internal angles in the triangles. With n vertices, each vertex is not directly connected to n-3 other vertices, thus n-3 diagonals can be drawn from a vertex which will create n-2 triangles (each with the sum of their interior angles as 180o); so: sum_of_interior_angles = 180 x (number_of_sides - 2)

apothem

In a 54-sided polygon, 53 possible diagonals can be drawn from one vertex to another. These diagonals will not intersect. Therefore, the interior will be divided into 54 regions by the 53 diagonals plus the two sides of the original polygon that adjoin the vertex from which the diagonals are drawn.

Circumscribed.

Apothem!

A concave polygon.