How many diagonals can be formed by using vertices of a polygon with 12 sides?
There is a polygon having 12 sides. So, number of vertices of the polygon = 12. From every vertex, (12 – 1 – 2) = 9 diagonals emerge out (excluding that particular vertex and the two vertices connected by two sides of the polygon extended out from that particular vertex).
How many vertices does a 12-sided polygon have?
In geometry, a dodecagon or 12-gon is any twelve-sided polygon….Dodecagon.
| Regular dodecagon | |
|---|---|
| Type | Regular polygon |
| Edges and vertices | 12 |
| Schläfli symbol | {12}, t{6}, tt{3} |
| Coxeter–Dynkin diagrams |
How many triangles can be formed by a 12-sided polygon?
For each side of the 12-gon, there are 12-4=8 non-adjacent vertices which you can use to form a triangle, so there are 12*8=96 such triangles.
How many sides does a 12-sided polygon have?
A dodecagon is a polygon with 12 sides, 12 angles, and 12 vertices. The word dodecagon comes from the Greek word “dōdeka” which means 12 and “gōnon” which means angle. This polygon can be regular, irregular, concave, or convex, depending on its properties.
How many diagonals can be formed by joining the vertices of the polygon having 8 sides?
20 diagonals
∴ The octagon has 20 diagonals. Hence, option C is the correct answer. Note: The octagon is a polygon in geometry, which has 8 sides and 8 angles.
What is the maximum number of diagonals that can be drawn to a Pentagon?
For example, a pentagon (5 sides) has only 5 diagonals. Each vertex has two diagonals, so if you counted each diagonal from every vertex twice, you might think there were 10 diagonals.
How many sides or faces are on a dodecahedron?
12
| Regular dodecahedron | |
|---|---|
| Type | Platonic solid |
| shortcode | 5d |
| Elements | F = 12, E = 30 V = 20 (χ = 2) |
| Faces by sides | 12{5} |
What’s a 12-sided object?
A dodecagon is a 12-sided polygon. In particular, a dodecagon with vertices equally spaced around a circle and with all sides the same length is a regular polygon known as a regular dodecagon.
How many triangles can be formed by joining the vertices of a decagon?
120
The number of triangles created by joining the vertices of a decagon is 120.
What is the difference between dodecagon and dodecahedron?
A dodecagon is a polygon (do for two, deca for ten, “gon”) with 12 sides. A dodecahedron is a solid with 12 faces (similar to tetrahedron, 4 faces). A dodecahedron is a 3-dimensional regular solid having 12 congruent regular pentagons as its faces.
How many segments does each vertex of a graph have?
There are 11 other vertices, vertex 2 through 12, with which it can form a segment. So, we have 11 segments radiating from vertex 1. Similarly, vertex 2 has 11 segments radiating.
How many segments can be formed from a four-sided polygon?
For a four-sided polygon, we have (4*3)/2 = 6 segments, which you can easily draw and convince yourself is correct. Similarly, for any other N-gon. This is the number of unordered pairs that can be formed out of 12 elements.
How do you number the vertices of a 12-gon?
Number the vertices of the 12-gon 1 through 12. Consider two cases for a valid triangle: Vertex 1 is not on the triangle. In this case, consider getting the 12-gon by starting with a 9-gon and putting 3 triangle vertices between the existing 9 vertices. There are $\\binom{9}{3} = 84$ ways to do this.
How do you make a 12-gon graph with one vertex?
Vertex 1 is on the triangle. In this case, consider getting the 12-gon by starting with a 10-gon consisting of vertex 1 and the 9 other vertices which are not triangle vertices. Then the remaining 2 triangle vertices can go between vertices 2 & 3, 3 & 4., 9 & 10, so there are 8 places to put them.