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To determine how many heptagons can be formed by joining the vertices of a 10-sided polygon, we can use the combination formula. Specifically, we need to choose 7 vertices from the 10 available. This is calculated as ( \binom{10}{7} ), which is equal to ( \binom{10}{3} ) (since choosing 7 vertices to include is the same as choosing 3 vertices to exclude). Thus, ( \binom{10}{3} = \frac{10!}{3!(10-3)!} = 120 ). Therefore, 120 heptagons can be drawn by joining the vertices of a 10-sided polygon.
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What is a line segment drawn between two points of a polygon in the interior is called what?
A line segment drawn between two points of a polygon that lies entirely within the polygon is called a "diagonal." Diagonals connect non-adjacent vertices of the polygon, providing a way to explore the internal structure of the shape. In contrast, line segments that connect adjacent vertices are referred to as the sides of the polygon.
How many diagonal can be drawn from a regular hexagon from one vertex?
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.
How many diagonals can be drawn from one vertex of a 12 sided polygon?
10 ... any polygon it is 2 less than the number of sides or vertices wince they are the same.
What is the number of diagonls which can be drawn by joining the angular points of a polygon of 100 sides?
It consists of 98 triangles and has 4850 diagonals
What is the line segment joining the opposite vertices of quadrilateral?
The line segment joining the opposite vertices of a quadrilateral is known as a diagonal. Each quadrilateral has two diagonals, which can be drawn by connecting pairs of non-adjacent vertices. Diagonals help in analyzing the properties of the quadrilateral, such as area and symmetry, and can also be used in various geometric calculations.
How many heptagons can be drawn by joining the vertices of a polygon with 10 sides?
120
How many pentagons can be drawn by joining the vertices of a polygon with ten sides?
10c5
What is a line segment drawn between two points of a polygon in the interior is called what?
A line segment drawn between two points of a polygon that lies entirely within the polygon is called a "diagonal." Diagonals connect non-adjacent vertices of the polygon, providing a way to explore the internal structure of the shape. In contrast, line segments that connect adjacent vertices are referred to as the sides of the polygon.
How many diagonal can be drawn from a regular hexagon from one vertex?
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.
What is this a line drawn between 2 vertices which are not next to each other?
This is a diagonal line. The definition of a diagonal is a line that joins two nonconsecutive vertices or corners of a polygon.
How many diagonals can be drawn from one vertex of a 12 sided polygon?
10 ... any polygon it is 2 less than the number of sides or vertices wince they are the same.
What is the number of diagonals that can be drawn from one vertex in a convex polygon that has n vertices?
N-2 according to yahoo answers
What is the number of diagonls which can be drawn by joining the angular points of a polygon of 100 sides?
It consists of 98 triangles and has 4850 diagonals
What is the line segment joining the opposite vertices of quadrilateral?
The line segment joining the opposite vertices of a quadrilateral is known as a diagonal. Each quadrilateral has two diagonals, which can be drawn by connecting pairs of non-adjacent vertices. Diagonals help in analyzing the properties of the quadrilateral, such as area and symmetry, and can also be used in various geometric calculations.
How many diagonals can be drawn from a vertex of an n gon?
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.
What is the formula for the number of diagonals in a polygon?
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
How do you find diagonals in a polygon?
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
