Define Convex Polygon

Author: mathqa22

In polygon comprise no reflex angle, followed in it is made-up to be a convex polygon. Polygon is a plane, that type to be restricted in a closed path, composed of a restricted series of directly line element by a closed polygonal series. Now we study about define convex polygon.

Using online polygon is a plane type to be restricted in a closed path, composed of a restricted series of directly line element by a closed polygonal series.

Define convex polygon:

A polygon is absolutely convex if every interior position is definitely less than 180 quantities. Commonly, a polygon is definitely convex if each line division by two noncontiguous vertices of the polygon is exactingly internal to the polygon however on its endpoints. Each non part triangle is definitely convex.

A polygon is a 2-dimensional instance of the more general polytope in several quantities of proportions. The internal of the polygon is recognized its group. These fraction are known its edges, with the points where two edges obtain together are the polygon's curve.

Commonly, a polygon is definitely convex if each line division by two noncontiguous vertices of the polygon is exactingly internal to the polygon however on its endpoints

Properties of convex polygon:

A convex polygon is an easy that's within is a convex set. The properties of an easy polygon are all equal to convexity:

Each one interior angle is less than 180 degree.

Each one line segment among two vertices remains inside or on the maximum of the polygon.

Examples for define convex polygon:

Example 1 for define convex polygon:

How to solve area of the polygon learning the sides are (6,3) (9,3)(7,5)

area of the polygon learning the sides are (6,3) (9,3)(7,5)

Solution:

Step 1: the given sides are (6,3) (9,3)(7,5)

Step 2: A =     1/2((x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+.......(x_ny_1-x_1y_n))

Step 3: x1=6, y1=3, x2=9, y2=3, x3=7, y3=5,

Step 4:     A =1/2(18+45+35)-(27+21+30)

Step 5:         so area is A =10

Example 2 for define convex polygon:

How to solve area of the polygon learning the sides are (7,2) (7,4) (6,5)

area of the polygon learning the sides are (7,2) (7,4) (6,5)

Solution:

Step 1: the given sides are (7,2) (7,4) (6,5)

Step 2: A =     1/2((x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+.......(x_ny_1-x_1y_n))

Step 3: x1=7, y1=2, x2=7, y2=4, x3=6, y3=5,

Step 4:      A =1/2(28+35+12)-(14+24+35)

Step 5: so area is A =1

Check this icse syllabus 2013 awesome i recently used to see.

Example 3 for define convex polygon:

How to solve area of the polygon and  prepare the sides are (7,6)(6,4)(6,2)

area of the polygon and prepare the sides are (7,6)(6,4)(6,2)

Solution:

Step 1: the given sides are (7,6)(6,4)(6,2)

Step 2: A = 1/2((x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+.......(x_ny_1-x_1y_n))

Step 3: x1=7, y1=6, x2=6, y2= 4, x3=6, y3=2,

Step 4:    A =1/2(28+12+36)-(36+24+14)

Step 5:         so area is A = 1

Normally in geometry polygon mean a plane figure which is closed by a line. Here we are going to learn about name of all polygons. We will name the polygons based on their number of sides. We will see the name of the polygons.  Totally we are having three types of polygons that are regular, irregular and equilateral polygons.

Name of all polygons:

Here we are going to name all the polygons based on their number of sides.

If any polygons having 3 sides we can say it is Triangle.

If a polygons with 4 sides we will say it is a Quadrilateral.

If a polygon is having 5 sides it is known as Pentagon.

If a polygon is having 6 sides it is known as Hexagon.

If a polygon is having the number of sides 7 then we can say it is Heptagon.

If any polygon is having the number of sides 8 then we can say it is Octagon.

If a polygon is having the number of sides 9 it is known as Enneagon or Nonagon.

If any polygon is having the number of sides 10 it is known as Decagon.

Name of all polygons: Sides above 10

If the number of sides is 11 then it is known as Hendecagon.

If the number of sides is 12 then it is known as Dodecagon.

If the number of sides is 13 then it is Tridecagon.

If the number of sides is 14 then it is known as Tetdradecagon.

If the number of sides is 15 is known as pentadecagon.

If the number of sides is 16 then it is known as Hexadecagon.

The number of sides of the polygon is 17 it is known as Heptadecagon.

The number of sides is 18 then we can say it is a Octadecagon.

The number of sides is 19 then we can say it is a Enneadecagon.

The number of sides is 20 then we can say it is a Icosagon.

Number of sidesName of the polygon

20Icosagon

30Triacontagon

40Tetracontagon

50Pentacontagon

60Hexacontagon

70Heptaconatagon

80Octacontagon

90Enneacontagon

100Hectagon

1000Chiliagon

10000Myriagon

1000000Hecatommyriagon

Article Source: http://www.articlesbase.com/k-12-education-articles/define-convex-polygon-6615656.html

About the Author

Learn more on about Online Volume Conversion and its Examples. Between, if you have problem on these topics Testing Bias, Please share your comments.

Online Basic Geometry Definitions

Author: Omkar

Introduction to online basic geometry definitions tutor:

In this article online basic geometry definitions tutor,we will learn some important geometry definitions they are necessary to understand geometry concept.Those basic geometry definitions are used to design a graph with the assistance of those terms. Tutor will teach to individual and guide them to get the solution for problems through some websites via online. Online is a tool for self-learning from websites.

Basic definitions- online basic geometry definitions tutor

Supplementary angles:

We can call any two angles as supplementary angles,if the sum up of them should be 180°

Complementary angles:

We can call any two angles as complementary angles,if the sum up of them should be 90°

Acute triangle:

An acute triangle means a triangle in which all three angles should be less than 90°.

Obtuse triangle:

Obtuse triangle means one type of triangle in this one angle must be greater than 90°.

Right angle triangle:

A right angle triangle means one type of triangle in which one angle must be a right (90°) angle.

Triangle Inequality:

The triangle inequality means the addition of any two side should be greater than the third side

Scalene Triangle:

A scalene triangle means a triangle with three different unequal length of side.

some more definitions- online basic geometry definitions tutor

Centroid:

The centroid means a point in which three lines will meet each other. This point is a center point of a triangle. If we cut a triangle corresponds to that center we will get three equal parts.

Circle:

In circle the distance between the center and to any point present in the outer line of a circle is same.

Radius:

Radius of a circle is the distance between the circle's center and any point present on the circle.

Circumcenter:

In a triangle three perpendicular line drawn from the three sides bisect each other . That point is called as circumcenter.From this center point we can draw a circle

Congruent:

Two figures are said to congruent when all the parameters should be same interms of length and angles.

Altitude:

An altitude means a line connecting a vertex to the opposite side.

Vertex:

Vertex means a point.

Transversal:

A transversal means a line which passes through two another lines there is a no issue that should be parallel.

Point:

A point indicates a single location

Plane:

Plane is a flat, two-dimensional object one.

Quadrilateral:

Quadrilateral is defined as a polygon and has exactly 4 sides.

Trapezoid:

A trapezoid means a quadrilateral which contain one pair of opposite side they should be parallel to each other.

Polygon:

A polygon means a two-dimensional geometric object.It is made up of a straight line segment those segments touches at the ends.

Rectangle:

Rectangle means a quadrilateral and should has 4 right angle.

These are the few terms for online basic geometry definitions tutor

Article Source: http://www.articlesbase.com/k-12-education-articles/online-basic-geometry-definitions-6615588.html

About the Author

Comprehend more on about Graphing Linear Equations and its Circumstances. Between, if you have problem on these topics acute scalene triangle Please share your views here by commenting.

Types of Pentagon

Author: nitin.p070

A pentagon is a closed two dimensional figure that is the union of line segments in a plane. A pentagon has the five sides and five angles. The internal angles in a simple pentagon total 540°. A pentagram is an example of a self-intersecting pentagon. A regular pentagon has five Edges and five vertices. Internal angle of a regular pentagon is 108 degree. There are two types of pentagons : concave pentagon and convex pentagon.

In geometry an equilateral pentagon is a polygon with five sides of equal length. Its five internal angles, in turn, can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique, because it is equilateral and moreover its five angles are equal.
Four intersecting equal circles arranged in a closed chain are sufficient to determine an equilateral pentagon. Each circle's center is one of four vertices of the pentagon. The remain vertex is determined by the intersection of the first and the last circle of the chain.

It is possible to describe any equilateral pentagon with only two angles a and ß with a = ß provided the fourth angle (d) is the smallest of the rest of the angles. Thus the general equilateral pentagon can be regarded as a bivariate function f(\alpha,\beta) where the rest of the angles can be obtained by using trigonometric relations. The equilateral pentagon described in this manner will be unique up to a rotation in the plane.

Types of Pentagon : Concave and Convex Pentagon:

Concave pentagon:

It is a five sided polygon. At least one interior angle is greater than 180 degrees.

This causes some of the vertices of the pentagon to points towards the center.

An alternate definition exists a line that will cut the polygon in 4 or more places.

The twelve concave pentagons can be get together to make a concave dodecahedron.

Convex pentagon:

It is a shape with 180degrees or less.

The regular pentagon is the example of the convex pentagon.

Let us see regular pentagon in detail.

Express your views on the topic 9th cbse sample papers 2011 by commenting on articles.

Types of Pentagon : Regular Pentagon

A shape with five equal sides and five equal angles are called as Regular Pentagon.

Properties of Regular Pentagon:

• It has five equal sides
• It has five equal angles
• It has five lines of symmetry

Angle of a Regular pentagon:

Exterior angle of any polygon is 360° and hence the exterior angle of a regular pentagon is 360°.

Regular pentagon has five sides so each exterior angle measures (360/5) = 72°.

Interior angle of a polygon is calculated by using the formula,
n - 2 (180)

Where n =number of sides.

Where n =number of sides.

Here for pentagon interior angle = (5 - 2) 180 = 540°.

For regular pentagon each side interior angle = 540 / 5 = 108°.

Area of any regular polygon is:

A = 5t2 tan (54) / 4

Derivation of the diagonal length formula:

D = T * (1+v5) / 2

Article Source: http://www.articlesbase.com/online-education-articles/types-of-pentagon-6278397.html

About the Author

Understand more on about the How to find the Center of a Circle, and its Illustrations. Between, if you have issue on these Geometry Angles keep verifying my content i will try to help you. Please discuss your feedback.

Polygon definition

Author: Matthew David

Introduction
Polygon

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. In geometry a polygon it can be traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners.

In geometry a polygon  is usually a plane shape  that is bounded by a closed  circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called edges or sides, and the points where two edges meet are the polygon's vertex or corners. A polygon is a 2-dimensional.Polygons is primarily classified by the number of sides.

Characteristics of Polygon

Convexity

Polygons may be characterized by their degree of convexity:

Convex: any line and it can be drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice.
Non-convex: a line may be found which meets its boundary more than twice.
Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
Concave: Non-convex and simple.
Star-shaped: the whole interior is the visible from and that is a single point, without crossing any edge. The polygon must be simple, and may be convex or concave.
Self-intersecting: the boundary of that  polygon crosses itself. Branko Grünbaum calls these Coptic, though this term does not seem to be widely used. The term complex is sometimes that can be used in contrast to simple, but this risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions.
Star polygon: it is a polygon which can be self-intersects in a regular way.

A digon is a closed polygon having two sides and two corners. On the sphere, we can mark two opposing points (like the North and South poles) and join them by half a great circle. Add another arc and it can be a different great circle and you have a digon. Regular Polygon Usually two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments will be considered parts of a single edge. A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees.

Special Nmaesof Polygons

Some polygons have special names and that are depending on the number of sides they have.



Number of sides              Name of polygon

3                            Triangle

4                            Quadrilateral

5                            Pentagon

6                            Hexagon

7                            Heptagon

8                            Octagon

9                            Nonagon

10                           Decagon

Classifying Polygons:

There are two categories of polygon. They are convex and concave. Polygons are also classified by the number of sides they have. The following list shows that the polygon name and number of sides they have.  

Triangle - three-sided polygon.

 Quadrilateral - four-sided polygon.

 Pentagon - five-sided polygon.

 Hexagon - six-sided polygon.

 septagon -seven-sided polygon.

 Octagon - eight-sided polygon.

 Nonagon - nine-sided polygon.

 Decagon - ten-sided polygon

Regular polygon:

A regular polygon is a polygon which has equal angles  and equilateral . Regular polygons may be convex or star.
Regular convex polygons:
1. Introduction to Square:

A square is one of the regular quadrilateral.  it has four equal sides and four equal angles .All angles are 90 degree .The total internal angles of square is 360 degree.

Square
2.Introduction to Equilateral triangle:

An equilateral triangle is one type of polygon.it has three sides.They are equal in length and the total internal angle of triangle is 180 degree.All the three angles are equal.(each 60 degree).

Equilateral triangle

3. Introduction to Pentagon:

The five sided polygon is known as pentagon. The sum of internal angle of a pentagon adds up to 540 degree. The all internal angles are equal( each 108 degree)

Pentagon
4.Introduction to Hexagon:

The six sided polygon is known as hexagon with equal length (regular hexagon).the sum of internal angle of a hexagon adds up to 720 degree. The all internal angles are equal (each 120 degree).

Hexagon

Article Source: http://www.articlesbase.com/k-12-education-articles/polygon-definition-6491446.html

About the Author

Between, if you have problem on these topics what are linear equations, please browse expert math related websites for more help on Area of a Triangle and different math topic.