Quick Answer: How Many Vertices Does An N Sided Polygon Have?

How many diagonals does an N sided polygon have?

The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides.

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)..

What is an n sided polygon?

An n-gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly.

What is a polygon with 5 vertices and 3 sides?

SidesName3Triangle4Quadrilateral5Pentagon6Hexagon5 more rows

How many diagonals does a 9 sided polygon have?

6 diagonalsSince there are 9 vertices in all, that’s a total of 9 – 3 = 6 diagonals we can draw: Since there are nine vertices, we should be able to do this nine times, right?

What polygon has 3 vertices and 4 sides?

A quadrilateral has 4 sides and 4 vertices. No shape has 4 sides and 3 vertices ( corners), unless you say a triangle has an inside, outside, front. 1:square 2:Rectangle 3: rhombus 4:trapiziod.

What is the name for a polygon with four vertices?

In Euclidean plane geometry, a quadrilateral is a polygon with four edges (sides) and four vertices (corners).

How do you find the interior angle of an N sided polygon?

Interior and exterior angle formulas:The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180.The measure of each interior angle of an equiangular n-gon is.If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.

How many diagonals does a 6 sided polygon have?

Classifying PolygonsPolygon NameNumber of SidesNumber of DiagonalsQuadrilateral42Pentagon55Hexagon69Heptagon7147 more rows•Jul 18, 2012

What polygon has 4 sides?

Four-Sided Polygons – Quadrilaterals Four-sided polygons are usually referred to as quadrilaterals, quadrangles or sometimes tetragons. In geometry the term quadrilateral is commonly used.

What is diagonal formula?

The formula to find the number of diagonals is n(n – 3)/2, where n is the number of sides the polygon has.

How many vertices are there in a hexagon?

6Hexagon/Number of vertices

How many diagonals does a 15 sided polygon have?

90 diagonalsTherefore, there are 90 diagonals in a 15 sided polygon.

How do you find the N sided polygon?

Divide 360 by the difference of the angle and 180 degrees. For the example, 360 divided by 15 equals 24, which is the number of sides of the polygon. Divide 360 by the amount of the exterior angle to also find the number of sides of the polygon.

How many degrees does an N sided polygon have?

The General RuleShapeSidesSum of Interior AnglesOctagon81080°Nonagon91260°……..Any Polygonn(n−2) × 180°6 more rows

How many vertices would a 20 sided polygon have?

20 verticesA 20-sided polygon has 20 vertices. The diagonals can be counted as AB , AC , AD , …, BC , BD , BE , …, ST , the combination of choosing 2 points from 20 vertices, or 20C2=(202) .

How many diagonals does a regular hexagon?

Number of Diagonals = n(n-3)/2 For example, in a hexagon, the total sides are 6. So, the total diagonals will be 6(6-3)/2 = 9.

What shape has more than 6 vertices?

hexagonThis is a hexagon. A hexagon has 6 angles, 6 sides and 6 vertices. This is an octagon. An octagon has 8 angles, 8 sides, and 8 vertices.

How many diagonals are there in polygon of 12 sides?

54 diagonalsSoooooooo we can draw 54 diagonals in a 12 sided figure.