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

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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

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Song for Kids About Caring

Song for Kids About Caring
By Jennifer Ruth Russell

How do you teach your child about caring?

What would this world look like without caring? What if we forgot how to care for each other?

Nothing would matter. We would all feel alone and unloved. People wouldn't care if someone else was in danger or had their feelings hurt. We would start being really sloppy in the way we did everything. We'd start doing things half way. Everything would start falling apart.

So what's the best way to teach a child about caring? Of course I will always tell you that one of the easiest ways for a child to learn is through song. Songs for children, that are easy to sing, help bring the left and right hemispheres of the brain together which gives them a 'happy' brain that is ready to learn.

Here are a few simple ways to let your child know they are already doing a good job of caring and will give them some ideas to boost their caring.

1. Take care of yourself. Treat your body with respect and kindness. Basic grooming is a way of taking care of yourself. Get plenty of sleep. Find a friend to talk to when you're sad. Singing a song for kids can make you feel happy too. Leave a conversation or a situation if it doesn't feel right.

2. Take care of your loved ones. Show your care and concern for those you love by listening to them while they're talking. Ask simple, caring questions like, "How are you doing?" Take care of the earth by recycling and picking up trash.

3. Take care of others who seem sad or lonely. Recognizing someone else's sadness by just being with them can be really helpful. Include them in what you are doing, like singing a song for kids. This can lift their spirits right away. Saying a prayer for them will not only help them but make you feel better too.

Taking care of a pet is one of the best ways to teach a child about caring for others. Also, simple chores that help take care of the unity of the classroom or household are esteem and care builders.

"Be gentle, be loving and handle with care. Those who need tender attention and prayer. Take care of yourself, take care of your loved ones. Take care of those suffering alone or in pain." These lyrics for the kids song, Caring are a good reminder for all of us.

Jennifer Russell is an award winning songwriter, founder and director of This is Where I Live Community Sing-along. She has written some excellent, empowering & fun songs for children that bring out their best qualities. http://www.rembakids.com

To date, This is Where I Live Community Sing-along, has reached over 10,000 children in 500 schools throughout the world. As a Community Arts Partner of the Los Angeles Unified School District, this program has proven its success in classrooms throughout the city.

http://www.rembakids.com/

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Distance Learning Courses - An Accessible Way To Training And Valuable Qualifications

Distance Learning Courses - An Accessible Way To Training And Valuable Qualifications
By Rajni Nayak

Distance learning is a respected system of education whereby a person can attain further education without the need of his/her physical presence in a college or university building. Sometimes someone has not been to school or college for a long time or has not been able to take formal education owing to certain reasons. Distance learning is a way of getting needed education from various distance learning institutions across the globe. The variety of content, qualifications and facilities to provide different distance learning courses is enormous. Renowned colleges and institutions in the UK and abroad are providing with respected accredited distance learning courses, which can help individuals to change career, get a promotion, gain more security or improve their earning potential in their existing job.

Many professionals opt for distance education whilst working which provides them with an opportunity to add to their knowledge, understanding and skills whilst still being employed and earning a salary.

Lifelong Learning

Humans have an inbuilt desire to learn about the world around them, to understand subjects they are interested in and to make progress through that learning process. But there are many students who for various reasons were unable to go to a school or performed poorly when in the traditional education system. Home learning courses can help in these cases because the students do not have to travel but can study at their own pace in the privacy of their own home. The whole range of subjects at every level from basic foundation courses through to respected degrees can be studied through distance learning institutions and colleges.

People of all age groups can and do take advantage of home learning courses, enjoying their time acquiring new and exciting knowledge. Women at home can pursue courses of their choice while taking care of their families and many household duties. It has been a great opportunity for people in remote areas to be educated at affordable prices from good city universities thus improving the likelihood of getting interesting and good paying jobs.

Methods of teaching in distance learning courses

The initial way that distance learning courses were delivered was by post. It involved courses being split into small sections and written in an easily understandable manner that the student could absorb and learn from. Whilst this method still exists the internet and advances in technology have introduced many other and more efficient ways to deliver distance learning courses. Videos are used to illustrate and explain the most complex of subjects, podcasts are extremely efficient in conveying less complex matters but the advantage of both of these techniques is that the student can watch or listen as many times as they need to grasp the concepts being conveyed. Webinars are now extremely popular and whilst saving travel time and expense still offer the camaraderie of "class" tuition. Home study courses have become a world-wide phenomenon, available to all, respected by academics and businessmen alike.

Distance learning courses have become a most desirable way to broaden educational access while improving the quality of training. They have transformed the educational system to make reputable learning and qualifications available to everyone Home Study Zone

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High School Math Can Be Fun

High School Math Can Be Fun
By Lance Merlino

Mathematics is known as the language of physics, and it is a very important part of everyone's life. Mathematics is used in all facets of life. But, one of the problems with math is that it is termed as a difficult subject. Even before students learn the subject or even are exposed to it, they are filled with the presumption that math is very difficult. But, the fact of matter is that math is a very simple subject if it is taught properly, and if the student understands it from the basics. Here are a few tips to make high school math fun.

Diagrammatic Explanation

Figures and diagrams are used very often in mathematics. That is because describing a problem in terms of figures will give you a better understanding of the problem. In case a student does not follow the question with the diagram, the answer can be depicted diagrammatically, and can be explained to the student more clearly. Most of the times, this method works fabulously, with students who find math difficult. So, it is always important that a maths tutor is able to diagrammatically represent both a question and its answer.

Number Games

Using number games is a very old and effective ways of teaching math to students, who feel that math is hard. There are different types of number games that the maths tutor can come up with. For example, when teaching probability, you can use the example of having a set of colored balls in a box. You can work out how you want to convey the concept to the students. Similarly, there are other number games that you can choose from books, or devise on your own, to teach math to students.

Team Activities

There is also another way of teaching math, where you split the students into teams and set them up against each other. This will breed a competitive spirit among the participants, and motivate them to help each other out, to learn the concepts and be better than the other team. However, you will need a set of students, at least 4, for this type of approach.

Real Life Examples

You can also use real life examples to make students understand math concepts. This approach is a little tricky, as it involves a lot of homework for the maths tutor. But, once the tutor gets a hang of this approach, this is one of the most effective ways of teaching math.

Lance Merlino is an expert maths tutor with Maths Success and has a long list of math help success stories of science students.

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Vocabulary, Education and Success - How Are They Related?

Vocabulary, Education and Success - How Are They Related?
By Lee W Reed

We are told that the average high school graduate has a vocabulary of 10 to 12 thousands words. I usually tell the middle school students I teach that they most likely have a vocabulary of about 8 thousand words. That's probably about right, though we can't help but wonder what texting is doing to our kid's vocabulary. Research done some years ago indicated that the average phone call used no more than 800 different words. How this research was done, I don't know, but it is an interesting factoid.

College has a profound effect on our vocabulary. There we have to read a great deal of the writings of highly intelligent people with great vocabularies and that has the effect of increasing our list of words we use. As a matter of fact, there is a stereotype of a newly minted college student who returns home and wishes to impress his/her friends with a host of new words. Eventually we learn that the real purpose of our speech is to communicate and we put aside the fancy words in place of those that will be effective with our audience. Nevertheless, by the time a student graduates from college they should have a vocabulary of close to 20 thousand words; nearly double what they had when they graduated high school.

All this talk of vocabulary begs another question: Exactly how many words are there in the English language? As it happens, English may be the richest of all languages when it comes to words. We have borrowed words from other languages and added many of our own until the Oxford English Dictionary lists 615 thousand words in our language. By comparison, German has just 185 thousand and French just 100 thousand. Winston Churchill is said to have had one of the greatest vocabularies of our time and he probably knew far fewer than half the total (perhaps close to 80,000.) Shakespeare had an exceptional grasp of the language and use over 60 thousand in his works. Some people who have particularly large vocabularies, especially those who read and write a great deal, have in the neighborhood of 60 to 80 thousand words. Typically, they make a game of learning new words, so to them, finding a new word they can use is like finding buried treasure.

One of the astonishing things about vocabulary is the number of words students have to learn in medical school. I mentioned that the average college graduate knows about 20 thousand words. The average medical doctor possesses a 40 thousand word vocabulary. Another doubling of the words they use in just a few short years. This is indicative of the intense learning these students do as they work their way through medical school.

There are number of voices out there that will tell you that people who have large vocabularies tend to be more successful than those who do not. The implication is that your paltry word skills are holding you back and if you just memorized more words you, too, could be successful. This is shaky logic at best. I suspect the reason that many people who are successful have large vocabularies is because they have graduate degrees to go with them. They also tend to read a great deal. Simply learning all the words these folks know will not give you their wisdom or judgment, which is why they were given there positions of authority in the first place.

One of the amazing things that is happening on the Internet right now is that prestigious schools are beginning to offer their coursework for free online. MIT was a pioneer in this area as the posted all the classes necessary to earn a degree in engineering from their school, online and free of charge. Of course, you would still need to buy the books, and they are not cheap, but you could ostensibly learning everything an MIT grade knows for a small fraction of the cost. By this method, you could not only learn all the words of a graduate, but also learning the principles that go with them. What you would not get for your efforts is a degree. For that you would have to pay all the usual matriculation fees.

It's an interesting thought; what could you do with an engineers training, but no degree? The jury is still out on that decision, but several students are giving it a try. It will be interesting to watch this trend in the future to see how things work out. One thing is certain, many other school have followed MIT's lead and are offering similar courses, including Harvard, Berkley, McGill and a host of others. It's a trend worth watching.

Lee Reed is a logophile, word lover, who has a respectable grasp of the English language and loves to write about it as well as the interesting things he has learned in his numerous travels. You can find more of his words at: http://teachingadayatatime.wordpress.com/

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