The Advantages of a Tutor Zone

The Advantages of a Tutor ZoneYou can call it a travel guide, and it will help you decide if a tutor zone is right for you. A tutor zone is a great way to help you find the right place for you, since you will be at ease in their arms.The primary advantage of a tutor zone is that you will get a new environment in which to do homework or other assignments. Since you are in a relaxed setting, this will allow you to concentrate more on your work.Sometimes, you may feel that a tutor zone is not for you. There is a real possibility that you are not comfortable with small rooms, traffic jams, other students or other distractions. If you have other choices, you should consider them first.You are very likely to be on a teacher's good side if you are a good student. Therefore, you will need to be conscientious of your performance. If you are a good student who takes his/her assignment seriously, this is one option for you. You may want to begin your studies in a room where you will not be dist urbed.Another option is a tutor zone that is very spacious. This option allows you to have your own space. You can choose a dormitory-style room, or you may want to live in a community home with other students. Either way, you will get a nice, warm place to call your own.It is important that you don't take your scholarship for granted, so you have to be fully committed to taking your course. You will be in a tutor zone for a long time, so don't give up easily.You can choose auto zone, even if you are from the United States. In fact, many people have discovered the wonders of traveling by plane. Now you can enjoy them in the comfort of your own home.

Start the School Year Off the Right Way With These Study Tips

Start the School Year Off the Right Way With These Study Tips Start the School Year Off the Right Way With These Study Tips The new school year is here! Start the year off right - develop a study schedule, organize your materials, and take a few moments to reflect on what you can do to make this year the best yet. Stay a step ahead Dont wait until you are behind to adjust your study skills. Starting the school year off the right way will provide you the opportunity to maximize your learning and stay ahead of your studies. Attend to your learning Good attendance is necessary for school success. Arrive at your classes early, make sure your materials are ready, and prepare for the days learning. Being ready beforethe school day and the individual class begins will help you acquire the most new knowledge. Review your study habits Think about your previous years study habits and determine what worked best for you. Talk to your teachers about any concerns you may have and how this years courses will impact your individual study habits. If you have laboratory based courses, such as chemistry, biology, or physics, seek additional time in the lab to review your learning with course materials on hand. Identify your strengths and weaknesses Understanding what your strongest academic areas are, and identifying the areas you struggle with the most, will help you plan your studying and maximize your learning. Huntington Learning Center can help. Each customized tutoring plan we create is based on the individual students strengths and weaknesses. Your tutoring plan will reflect your needs and is crafted based on your individual assessment data. Find What You Need Each student is different and what works best for you is personal. Some students choose to study in large chunks of time and others prefer to spread their studying out over time. You may study best at home in your bedroom but your friend may do better in a secluded corner of the public library. Determining your ideal conditions for studying will aid your preparation. Choose the perfect spot It is important to determine the perfect spot for you to study. All of these study tips will be irrelevant if your study location is insufficient. Where are you most comfortable? Which study spot has the least amount of distractions? Where do you complete your best work? Set a weekly schedule Take the time to create a master study schedule you can stick to each week. Be careful to schedule plenty of time around family, athletic, and extra-curricular activities. Consider building in extra time in case unforeseen circumstances or commitmen ts arise. Know when you need help If your school work is quickly becoming overwhelming and you are struggling to keep up it may be time to ask for help. The professional tutors with Huntington Learning Centers will administer assessments to determine your current strengths and weaknesses. Your progress will be carefully monitored to determine areas of continued need and the tutoring plan will be updated as you master new learning. Stay in Touch It is important to stay on top of both coursework and your individual performance. Knowing when you need additional support, and asking for help, is best done as soon as difficulties arise. If you wait too long to seek assistance you will likely be wasting precious study time. Review expectations Don't just read the syllabus and stick it in a folder. Your course expectations should be reviewed often to ensure you haven't missed any important dates or information. Compare the expectations periodically with your master calendar to make sure you haven't overlooked anything. Connect with others There may be other students in your class who are searching for a peer to connect with. Having another student in the class to study with, compare notes, and bounce ideas off of is a great way to stay connected with the academic work. Communicate with teachers and tutors Do your part to communicate with your teachers and tutors. When you are feeling confused ask for help. When something seems frustrating or overwhelming let them know. Utilize your teacher's office hours or review sessions and spend time during tutoring sessions to share your concerns or problems.

Who can be a Science tutor

Who can be a Science tutor Tutoring Science requires both practical and theoretical skills to ensure a lively and engaging tutorial style. More than any other subject, Science is as much about doing and seeing as it is about listening and understanding. Therefore those who can provide a high level of interaction will create a strong impression. It is for this reason that those people who come from careers with a high 'Applied Science' element are likely to make very good Science tutors. People who have worked as a laboratory assistant or researcher, an engineer or mechanic, will all have the necessary attributes to thrive in a tutorial environment. Of course, Science breaks down into a number of key areas and those who wish to tutor older students may come from a highly specialised background. For Biology, those with a background in botany, zoology or medicine can prove to make a successful crossover, while Physics tutors may benefit from a mechanical or technical background. In Chemistry, those with a background in the chemical industries, or combustion design will also have an advantage. If you are interested in tutoring Science, have a look at our section For Tutors. You'll find some handy hints on lesson planning as well as an overview of the things you need to take into consideration when advertising your services as a private tutor.

Strange Interview Questions (and How to Answer Them)

Strange Interview Questions (and How to Answer Them) Image via pexels.com 1) How can you use a pencil, other than as a writing instrument?   Personally, I remember being asked this in an interview and completely blanking out on the answer. I ended up saying that you could use a pencil to keep hair tied up if you did not have a clip or a hair tie on hand, which my interviewer said was a good and practical use of a pencil. I remember looking up alternate uses on the ride home, wanting to know if there were better answers  there, of course, was  this well-crafted answer. This questions purpose, like many other oddball questions, is to test your creativity on the spot. Potential employers want to see how you can approach something that has already been put in place and put your own take on it. They want to see what you can bring to the company and if you already have the potential in you to bring positive change to the company. 2) Take a common, everyday object and try to sell it to your interviewer This particular question can change interview to interview. Generally, your interviewer will get an everyday ballpoint pen and ask you to try to sell it to them using your own selling points and advertisement. Or, they can ask you to take something that you have on you (chapstick, a wallet, glasses case, etc.) and try to sell it to them. Either way, your response to this interview question can be very telling, especially if the position you are interviewing for involves marketing, advertising, or customer service. This interview question tests your creativity youre suddenly faced with the task of trying to sell an object that you regularly wouldnt give much thought to whenever you use it. It also can give the interviewer a look at how you would act with a potential customer your customer service, trying to adapt your selling routine to a specific customer, etc. For example, if you happen to be trying to sell lipstick, there are plenty of selling points other than using it as a lip color. You can use it for color anywhere blush, eyeshadow, temporary body paint. You can use it as an emergency writing utensil. You can use it as a survival item when youre lost on a trail or forest mark nearby trees or landmarks to mark where you have already been and avoid circling around the same area. You can hollow out the lipstick container and use it as storage for small trinkets like bobby pins in your bag. 3) Would you rather fight one horse-sized duck or 100 duck-sized horses?   This interview question is bizarre to both hear and imagine and like any bizarre interview question, it can also tell your interviewer plenty about you. The interview question tests your logic and reasoning. In some cases, you may ask if you are alone, if you have any weapons or protection, etc. Asking more questions shows your interviewer that you are willing to ask questions when you arent sure of something (which many people are hesitant to do). This question also tests your task management when you answer on how you plan to fight either choice. Is it a matter of endurance to fight one horse-sized duck? You can reason that fighting just one opponent is easier and safer because you have more control, rather than fighting a hundred different opponents. Youll be tackling one problem rather than drawing out the 100 small problems. On the other hand, does great planning help you defeat 100 duck-sized horses? If you can reason and explain a plan to solve each and every little problem, your answer will definitely highlight your task management skills to your interviewer.

13 free resources for ESL lesson planning I couldnt teach without

13 free resources for ESL lesson planning I couldn’t teach without So you think you can TEFL? And it’s true, you’ve got the certificate, you’re fully qualified and all set to teach English abroad or even teach English online. You ’ve got some lesson ideas under your belt. Maybe you’ve got more lesson ideas than you know what to do with, I was like you once… young, eager, the power of my TEFL notes clouding my vision. There are days when churning out another TEFL lesson plan is going to feel like an impossible feat. During my second week in South Korea, (a newly-minted teacher with lots of stickers and enthusiasm) I was asked to plan not one, not two, but fifteen weeks worth of 2-hour after school classes (that quickly put a stopper on my enthusiasm, and it quickly turned to blind panic. I don’t know if you’ve ever tried to fill up two hours with fun activities for bored fourteen-year-olds… but it’s hard enough when they speak your language, let alone when you will be miming 90% of the time. And then to plan 15 of those lessons….all at the same time. I was also told the principal would attend these classes. Just you know, to add to the overwhelming feeling of nausea. To say I almost had a heart attack is the understatement of the century. The 15 weeks’ worth of lesson plans weren’t due by the end of the month - they were due the very next day. You might think - sure, that would never happen to me. Who is this disorganized nincompoop? I bet they gave her loads of notice and she just forgot. But let me tell you, I am not a nincompoop. I color code my spreadsheets, I plan most things a month in advance and I don’t even find thrillers surprising. I’m a serial organizer. I like to make lists, tick off lists, you get the picture - LISTS are my particular way of life! I spent a dark, dark night planning those 15 lessons, the internet became my savior. Afterward, I sat back and thought - this is going to happen again, isn’t it? Rather than go to bed and sleep it off like a reasonable person. I made a list. This list was my way of coping with any last minute mass ESL lesson planning. Some of these resources helped me with regular lesson planning too. There are so many great teachers out there sharing ideas, exercises and activities for ESL students at every level. This list meant I could get inspiration on demand and even if a request for a truckload of lesson plans came through. I didn’t need to break out in a cold sweat. Although, I did anyway. Some of us are just born this way . All these resources are not created equal. Some are better for TEFL games, others for summer or winter camp activities, others will help you sort out those painful grammar classes. Never forget, there’s a whole community of teachers out there just like you, and everyone struggles with a lesson plan from time to time. So go forth and get some TEFLspiration. Yes, it’s a word, just go with it. 1. Pinterest If you use search words like “summer camp”, “ESL” or “TEFL, Pinterest is a treasure trove of ideas. I even used the DIY sections to build in craft activities for those longer after school camps or winter camps. Y’know those ambiguous periods where you’re half-teacher, half-babysitter, and 100% worried that the kids might get bored, stop paying attention and start eating potatoes (even though I’m Irish, this was a new one for me!) or stabbing each other with pencils (ditto…)??. And yes, I taught teenagers, why do you ask? 2. British Council One of the best things that ever happened to me was finding this website. From grammar exercises to helpful videos, to listening practice… there is no shortage of free TEFL lesson plans and ideas here. They’re also pre-graded and there are different sections for teaching adults, kids and teenagers. It’s a serial organizer’s dream! This website is also perfect for last minute planners or emergency classes (you know when there’s suddenly a class on your schedule that wasn’t there before). 3. Englishgrammar.org Not so much for lesson planning, more for those tricky questions advanced students or co-teachers might try to ask on the spur of the moment. “It just sounds right” won’t be a good enough answer and it can be hard to remember the trickiest rules of English (it’s a pretty fickle language) at a moment’s notice. This is also handy for some ideas on how to teach a few of the trickier tenses. It’s not going to set their eyes alight, but it will help you clarify exactly how to teach the harder bits. 4. ESL Partyland Don’t judge a website by its name, design, or layout! Trust me, the section on this site that’s dedicated to helping teachers is wholesome! From ways to incorporate music, games, video, and film, there’s no shortage of ideas to springboard your next ESL lesson plan. Just try not to cringe over the whole Partyland thing… TEFL turns the best of us into mildly cheesy grammar clowns. 5. My ESL Corner TEFL worksheets, lesson plans and games galore. This is a great little hub of ideas that will get your students excited about learning English. From lessons like creating your own restaurant to designing your own music magazine, this is a wonderful resource for some project-based learning. I particularly love the blog and it has lots of great articles, like this one on unique intro classes. 6. The Internet TESL Journal This website is amazing! It’s also quite ugly, but don’t let that put you off. What they lack in fancy design work, they make up for in sheer brilliant content. The lesson plans are life savers and if you’re looking for some interesting conversation class ideas - then you won’t be disappointed. There’s also plenty of articles and research on teaching techniques that will be invaluable in the classroom. 7. UsingEnglish.com When it comes to finding exactly what you want at the last minute - this site isn’t great. But it sure is worth a browse. If you pop into the teaching section, it’s divided by ESL levels, so you can easily find different types of games and lesson plans for students at different levels. 8. ThoughtCo Beautifully named, this site is perfect for some of those formal or business English classes, this collection of blogs has plenty of ideas for dialogue, conversations and class management. I quite like resources section where there are blogs on stuff like short speaking activities and fingerplay songs for kids. 9. ESL Galaxy This little site was great when it came to study classes, supervision and those times when you’ve got a clever clogs that is way ahead of the rest.??? You can easily print off some worksheets here that will keep even your highest level students busy, while you focus on getting the rest of the class caught up. When you’ve got 30 students in one room, and 40 minutes - sometimes a simple worksheet can give you valuable minutes. There’s nothing worse than watching a bright kid dying a little inside, so I always tried to keep mine on their toes. 10. ESLvideo.com Depending on where you’re teaching - YouTube and short online videos can be a HUGE resource. Even the potato-eaters paid attention when I played a clip. I used to trawl youtube for fun things my students might like and then build out quizzes and blank fills for them. But there are days when trawling the internet is not the best use of your time and this site already has videos and exercises sorted by ability level. So whether you’re looking for a song with appropriate vocabulary for your ESL students or a TED talk that won’t leave them scratching their heads, this is definitely a quick fix. Sign up to Teach Away today for access to the latest teaching jobs around the world. 11. BusyTeacher.org An oldie but a goodie! Busy Teacher is one of those sites where you can get some pretty interesting resources. As I write this one of the top worksheets of the week is Donald Trump’s Speech (Designed for Russian-speaking students!), But there are less niche resources and you can easily find some TEFL board games and worksheets that will pad out those lesson plans. 12. ESL Games World There’s nothing my students loved more than being tricked into learning with interactive games. This site is a great one if you’ve got access to computers. Everyone can work at their own level. Although I would only suggest computers in smaller classes where you can make sure they’re not just googling cute popstars. “Teacher, is he sexy?” - is technically English, but maybe not what I was setting out to achieve in my classes. The site has printables too, and everything is based around target language that you’re most likely going to be teaching. I found this site helpful for printables as I didn’t have access to much technology in most classes. 13. DUOLINGO It depends where you’re teaching. But I was in South Korea and there is an English for Korean speakers section. It’s worth checking it out. Gamification at its finest. Even my weakest kids loved to get 5 minutes on their phone to level-up. I positioned it as a reward, little did they realize they were learning! They’d often come up to me to show me a new lesson or unit they had completed. I had to walk the co-teachers through the app first. They were older and a little suspicious of the students learning English on their phones. One of my co-teachers became a bit of an addict! She absolutely loved getting her bonus points for perfection! It only keeps the students amused for 5 minutes and you can’t really use it for a whole lesson, but I got my students to make sure it reminded them to practice every day.

Three ways to attract teachers to vacancies

Three ways to attract teachers to vacancies Having trouble driving applications to your teaching job vacancies? It can be difficult for schools to find teaching candidates from thousands of miles away. Luckily, utilizing technology makes it easier for you to reach more applicants and attract a higher number of qualified candidates. Post your job on social media In the United States alone, 14.4 million job seekers have reported using social media to seek their next employment opportunity, and almost 30% of candidates say that social media is their primary source for leads on new jobs. If you’re not utilizing social media, you may be missing out on a significant percentage of candidates. Ensure that you have an up-to-date profile on sites like Facebook, Twitter, and Linkedin, and post new job vacancies to get the word out there! Revise your title and job description When writing job descriptions for an English-speaking audience, opt for a professional title and description. Avoid using exclamation marks in the title (“Great opportunity!!”) and making bold claims that you think will entice applicants (“Great salary! No visa required!!”). Instead, opt for a simpler, professional-sounding title, such as “ESL Teacher - Reputable Language Center in Shanghai.” As for the job description, keep it informative but brief. You’ll want to give candidates enough information so that they can decide whether to apply, but keep in mind that a job description is also a form of job marketing, and the text should be short enough so that they do not lose interest. You can give further details at later stages of the application process. Post a listing on Teach Away Smaller schools with a few vacancies should consider Teach Away’s job posting options. Advertising your job on Teach Away’s site means reaching a database of over 220,000 educators from around the world. For one flat fee, job postings stay on Teach Away’s popular job board for 30 days, with options to upgrade as well. Check out your options here, or talk to someone at Teach Away for more information. Happy recruiting!

Elements - The Math Equation

Elements - The Math EquationA little known fact about the elementary design math equations and their Elements is that they can be worked out in the different elements of a periodic table, called the Elements. This table represents the chemical elements of our world and has been widely used as a way to classify things. Elements are different than elements because they have different densities, and different compounds.Nowadays, you can work out elements in most science texts with the help of a formula such as Z = nCn, where Z stands for Zirconium, C stands for Cobalt, and n stands for Nitrogen. A proof will usually start from there, so what can be done if we know that? By using this equation we can now do the compound for Element A by taking the lowest value of the function ZZ or Z/C. The formula looks like a long equation in Arabic. We now have the formula to combine an Element A compound ZB/C.Next, we can see the Element A and find the Key that we need to break the formula down to El emental A and B. Since we are working with an abstract system, we can use the Natural Number System, which involves the symbols that are not mentioned above. When using natural numbers, we are using the same symbol every time, just replacing its value with one from the set, either positive or negative. For instance, A=1, B=0, which equals C=0, so A becomes C or vice versa. For the time being, we are going to use natural numbers for the element A, but there is a technique to create an Element A when we want to.Factorization is the easiest way to get the element. In fact, it is also one of the best ways to work out a formula that can be used for a given number. If we need an Element A, then we should use the formula C=A+a to work out the compound formula. Factorization can be easily explained. For the Base 10 scale, you simply multiply the coefficients of the natural numbers by the number. For instance, we could convert that C=x2, and then multiply the result by 10 to get an integer. Factoriation can be applied to any base. You might remember factorization being used in grade school math, especially when kids were doing fractions.Another way to think of it is to think of it as a geometric form. We can represent the elements as a regular diagram, much like a graph. In these diagrams, we are only going to write down the names of the elements. Instead of multiplying a formula by it, you would multiply a number by a certain number of horizontal lines. Then you divide it by the number of horizontal lines.As you can see, there are several ways to explain the Element Equation formula, but it is really just a formula. There are several ways to do the same thing, but it really depends on what your program allows you to do.

I.B. Chemistry I.E.I.A. Ideas

I.B. Chemistry I.E.I.A. IdeasIf you are a freshman or a sophomore, you might find I.B. Chemistry one of the toughest subjects to take, but if you have the right idea, it could become a breeze! In this article, I will give you an overview of some of the I.B. Chemistry I.E.I.A.I. Ideas that can change your whole life.First off, a lot of students focus on using Expos, their two studies A. I.B. Chemistry is the backbone of many research projects, and so why not capitalize on this opportunity by doing the best Expos? You should make the most of this opportunity and make the exam as easy as possible. Your exam grade will also benefit from completing these Expos.Second, some I.B. Chemistry students think that you can study the material better through the use of Expos rather than studying outside the classroom. This is probably not the best way to go, however, because Expos actually give you a much better chance at getting a great score on the I.B. Chemistry exam, so use them.Third, students who have taken several courses in college may struggle with the exam, and they tend to burn out. There are a lot of things you can do to speed up your studies, and I.B. Chemistry is one of them.Fourth, many students fail because they want to do well on the I.B. Chemistry exam, but are just not aware of the importance of taking adequate time for studying. Therefore, they end up over-scheduling themselves and losing precious time due to not knowing how to handle it. Even if you are working a regular job, you will still need to take enough time to study for the exam.Fifth, the I.B. Chemistry exam can be quite difficult. Therefore, I.B. Chemistry is not for everyone, but if you are certain that you will pass, you should definitely study for it very hard.Finally, there are some good I.B. Chemistry I.E.I.A. Ideas that you can take advantage of to help boost your score. Make sure you spend as much time as possible studying, and you will score far higher than if you didn't take the time to study!

Hexagon

Hexagon Hexagon Geometry is one of the most important branches of Mathematics as it deals with the study of different shapes, their dimensions, and calculations of them. In this study, we look at shapes formed by straight lines, and shapes which have curved surfaces. The 2-dimensional figures which have flat faces, which have straight lines as edges and which are closed are known as Polygons. Polygon family is a family consisting of different shapes of different number of sides. The word poly means many and gon means angle. Based on the number of sides a polygon has, we classify them into further categories. For example, polygons having 3 sides are known as Triangles, polygons having 4 sides are known as Quadrilaterals (rectangles, squares, etc), and polygon having 5 sides is known as a Pentagon and so on. A polygon which has 6 number of sides is known as a Hexagon. The word hexa means six and gon means angle. Since the polygon has 6 sides which consequently forms 6 angles, hence it is known as a Hexagon. Hexagon Definition: A polygon which has 6 number of sides (or edges) and 6 number of angles is a Hexagon. As shown in the figure on the left, hexagons have 6 vertices (or corners), 6 edges (or sides) and 6 angles. Types of Hexagons: Based on the measurements of the sides, hexagons are classified into 2 types: Regular Hexagons and Irregular Hexagons. 1) Regular Hexagons: A hexagon which has all the 6 sides equal in measure is known as a Regular Hexagon. Because it has 6 equal sides, the 6 interior angles of a hexagon are also equal. Properties: a) Regular Hexagons has 6 equal sides and 6 equal interior angles. b) As a hexagon has even number of sides, hence the opposite sides of a regular hexagon are parallel to each other. c) A line drawn from the center of the regular hexagon to any of the vertices will have the same length as the side length, as shown in the figure below. d) All the regular hexagons are convex, which means that all its 6 vertices point outward. e) The line segment joining any two non-adjacent vertices in a polygon is known as a Diagonal. The diagonals of a regular hexagon divide the hexagon into 6 equilateral triangles as shown in the figure on the right. 2)Irregular Hexagon: A hexagon which is not regular is known as the Irregular Hexagon. This implies, that an irregular hexagon has 6 sides that are not all equal in measure, or 6 interior angles that are all not equal in measure. Properties: a) Irregular Hexagons do not have 6 equal sides or 6 equal interior angles. b) The opposite sides may or may not be parallel to each other. c) An irregular hexagon can be convex in shape or concave in shape. A Convex polygon is a polygon which has all the vertices pointing outward. But in a concave polygon, one or more vertices point inward towards the center of the polygon. Because of this reason, in a concave polygon one or more interior angles is greater than 180. d) A line drawn through a concave hexagon (depending on where the line is drawn) can intersect the hexagon at more than 2 points. The below figure shows the line intersecting the hexagon at 4 points. e) In a concave hexagon, all the diagonal do not lie inside the hexagon. One or more diagonals lie outside the hexagon also, as shown in the figure below. Angles of a Hexagon: 1)Sum of all the interior angles of a Regular Hexagon: The sum of all the interior angles of any regular polygon can be calculated using the formula given below: If a regular polygon has n sides, then the sum of all its interior angles, S = (n 2) * 180 Since a hexagon has 6 sides, hence n = 6. Now Sum, S = (6 2) * 180 = 720 Therefore, Sum of all the interior angles of a regular hexagon, S = 720 2)Each Interior angle of a Regular Hexagon: The measure of each interior angle of any regular polygon can be calculated using the formula given below: If a regular polygon has n sides, then Each Interior angle = (n 2)/ n * 180 Since a hexagon has 6 sides, hence n = 6. So, Each Interior angle = (6 2) / 6 * 180 = 120 Therefore, Each interior angle of a Regular Hexagon = 120 3)Each exterior angle of a Regular Hexagon: The measure of each exterior angle of any regular polygon can be calculated using the formula given below: If a regular polygon has n sides, then Each Exterior angle = 360/n Each Exterior angle of Regular Convex Hexagon = 360/6 = 60 Therefore, Each exterior angle of a Regular Hexagon = 60 4)Diagonals of a Hexagon: Number of diagonals in a polygon of n sides = n * (n 3)/ 2 Since a hexagon has 6 sides, hence n = 6. Therefore, number of diagonals in a hexagon = 6 * (6 3)/2 = 9 diagonals. Perimeter of a Hexagon: Perimeter is the total length calculated when all the side lengths of the polygon are combined together. Perimeter of a regular or irregular polygon can be calculated by adding all the side lengths of the polygon. Perimeter of a Polygon = Sum of all its side lengths. Therefore Perimeter of a Regular Hexagon of side length s (as shown in the figure on the right) will be written as, P = s + s + s + s + s + s = 6s Example: Calculate the perimeter of a regular hexagon whose side length is 7m. Perimeter of a Regular Hexagon, P = 6 * s == Perimeter, P = 6 * 7m = 42m Example: Calculate the perimeter of the hexagon shown below. Given the side lengths of the hexagon in the figure. Perimeter of a Hexagon = Sum of all the side lengths. Therefore, Perimeter, P = 4m + 7m + 3m + 2m + 8m + 2m = 26m Area of a Hexagon: Area of any polygon is the space occupied within the boundaries or edges of the polygon. Hence, area of a hexagon is the space covered within its edges or sides. Area of a regular hexagon is different from the area of an irregular hexagon. Various procedures can be used in order to calculate its area. Let us look at the common methods used in the process. 1)Area of a Regular Hexagon: As mentioned above, diagonal of a regular hexagon divide the hexagon into 6 equal triangles, also known as 6 equilateral triangles. So if we find the area of one equilateral triangle, then the area of all the 6 triangles will be known, and then the area of the hexagon will be the triangle areas added together. Given a regular hexagon as shown in the figure above, where point C is the center of the hexagon. Triangle CPQ is an equilateral triangle, as all the angles inside triangle CPQ are equal to 60 (half of the interior angle 120). Hence all its sides are also equal. Therefore, let the side lengths of CP = PQ = CQ = s CM is the perpendicular drawn to the side PQ. Let CM = h As M becomes the midpoint of side PQ, hence MQ = s/2 (half of the side length of PQ). Now in triangle CMQ, we can apply the Pythagorean Theorem to get the relationship between the height h of the triangle, and the side length s. Hence, h2 + (s/2)2 = s2. This implies h2 + s2/4 = s2. This gives h2 = s2 s2/4 So, h2 = 3s2/4 == h = (3s2/4). Therefore, the height of the triangle CPQ, h = s* 3/2 Now, Area of triangle CPQ = 1/2 * base * height. This implies, Area A = 1/2 * s * h == A = 1/2 * s * (s * 3/2) == A = s2 * 3/4 Therefore, Area of triangle CPQ = s2 * 3/4. Now, a regular hexagon consists of 6 such congruent equilateral triangles. Hence, Area of a Regular Hexagon = 6 * s2 * 3/4 which can be further simplified as: Area of a Regular Hexagon = 3/2 * s2 * 3 Example 1: What is the area of a regular hexagon whose side length is 5m? Given that the side length, s = 5m Area of a regular hexagon, A = 3/2 * s2 * 3 Hence, Area = 3/2 * 52 * 3 = 3 which is 64.95m2 (approximately) 2)Area of an Irregular Hexagon: Since an irregular hexagon does not have equal sides or equal angles, hence we cannot use the method or formula of the regular hexagon. For an irregular hexagon, we can calculate area by using various methods. Let us look at an example below: Example: Find the area of the irregular hexagon shown in the figure below. In the given figure, we observe that the side lengths are given and the lengths of the diagonals are also given. We can see that the irregular hexagon is split into 4 triangles A, B, C and D. Since the side lengths of each triangle are given, we can use Herons formula. Herons Formula: If a triangle has side lengths as a, b and c, then s = (a + b+ c)/2 Then, Area of the triangle = [s* (s-a)* (s-b)* (s-c)] Triangle A: s = (5 + 4 + 7)/2 == s = 8 Now Area of triangle A = [s(s-a)(s-b)(s-c)] = [(8* (8 - 5) * (8 4) * (8 - 7)] Area of Triangle A = (8 * 3 * 4 * 1) = 9.8m2 Triangle B: s = (7 + 7 + 6)/2 = 10 Area of triangle B = [(10 * (10 - 7) * (10 - 7) * (10 - 6)] = (10 * 3 * 3 * 4) = 18.9m2 Similarly using Herons Formula as shown above, we get the areas of triangles C and D as well. Area of Triangle C = 8.9m2 and Area of Triangle D = 7.9m2 Now, Area of the Irregular Hexagon = Area of Triangle A + Area of Triangle B + Area of Triangle C + Area of Triangle D Area of the Hexagon = 9.8m2 + 18.9 m2 + 8.9 m2 + 7.9 m2 = 45.5m2 Hexagonal Tessellation: When a flat surface or a plane is covered by shapes that are repeated over and over again forming a periodic pattern, without any gaps or overlaps is known as Tessellation. We can find different kinds of tessellations such as tessellations of triangles, squares, rectangles etc. Regular polygons which are congruent (meaning same shape and size) form tessellations known as Regular Tessellations. There are only 3 types of Regular Tessellations, and they are of triangles, squares, and hexagons. A Hexagonal Tessellation is a tessellation formed when hexagons are arranged on a plane as shown in the figure below. This pattern for a Regular Hexagonal Tessellation is identical. In the figure below, we can see the vertex marked. At each vertex, we can observe that 3 hexagons are meeting. Since each hexagon has 6 sides, hence this kind of tessellation is named as 6.6.6 Tessellation. Hexagonal Prism: A hexagonal prism is a 3-dimensional figure consisting of 2 hexagonal bases and 6 rectangular faces. A hexagonal prism consists of 8 faces, 18 edges and 12 vertices. Because of its 8 faces, it is also known as the Octahedron. Surface Area of a Regular Hexagonal Prism: As shown in the figure below, a hexagonal prism has 2 hexagonal bases and 6 rectangular faces. Lateral area of the hexagonal prism is the sum of the areas of the 6 rectangular faces. If the height of the prism is h and the side of the base regular hexagon is s, then: Area of each rectangular face = s * h Lateral Area = Sum of the Areas of 6 Rectangular Faces Therefore, Lateral Area = 6 * s * h Surface Area of a Prism = Bases Area + Lateral Area The perpendicular from the center of the hexagon to its base side is also known as the Apothem (shown as d in the figure below). If the base side length is s, then as mentioned above Apothem or height of the hexagon is s * 3/2 Then, Area of the Hexagon = 3 * s * d = 3 * s * 3/2 * s = 3/2 * 3 * s2 Since there are 2 such base hexagons, hence Bases Area = 2 * 3/2 * 3 * s2 = 33 * s2 Surface Area = Bases Area + Lateral Area Hence, Surface Area of a Regular Hexagonal Prism = (33 * s2) + (6* s* h) (Where s is the side length of the base regular hexagon and h is the height of the prism). Example: How much is the surface area of a regular hexagonal prism if given the side length of the base regular hexagon is 4 inches, and height of the prism is 6 inches? Given that the side length of the base regular hexagon, s = 4 inches Height of the prism, h = 6 inches Surface Area of a Regular Hexagonal Prism = (33 * s2) + (6* s* h) Therefore, Surface Area = (33 * 42) + (6 * 4 * 6) = 483 + 144 = 227 square inches (approx.) Volume of a Hexagonal Prism: Volume of a Prism is the amount of space occupied within the boundaries or edges of the prism. Volume of a Hexagonal Prism = Area of the Base * Height of the Prism Therefore, Volume of a Hexagonal Prism = 3/2 *3 * s2 * h Example: Calculate the volume of a hexagonal prism whose base side length is 4 inches and height of the prism is 6 inches. Given that the side length of the base regular hexagon, s = 4 inches Height of the prism, h = 6 inches Volume of a Hexagonal Prism = 3/2 *3 * s2 * h Hence, Volume = 3/2* 3 * 42 * 6 = 249.4 cubic inches.