Writing Tutors Help a Lot

Writing Tutors Help a LotThere are a lot of benefits to hiring a writing tutor at a local college or university. First, you can do it yourself - and you won't have to worry about them trying to sell you on something you don't really need. And second, you can get one-on-one tutoring that will make you a better writer in the long run.Reading, writing, and speaking are among the most important skills any person can have. For example, I know a guy who has a hard time speaking English fluently - but he's really good at reading and writing. And when it comes to reading, he is at a disadvantage. Not, because he's old, or anything like that. But it's simply not his natural speaking voice that's preventing him from reading well.Well, that little thing is one of the main reasons he might not be as good at this as a kid who grew up speaking the language would be. It's just that the phonics in English didn't come with the language when he was born. If it came later, his mouth is wired differentl y than a younger generation's mouth is wired.And when he looks at English, he's looking at words. While the phonics have been worked out, the letter and spelling systems for the language haven't been - because when the written form was created, it was only done so the foreign languages could write the English language.So while it's easy for him to read, his comprehension level is somewhat limited. I never went to a public school, but I would assume that he'll have some kind of 'learning style' to him - it's almost as if the way he learns is a side effect of being born that way. One of the best ways to teach somebody how to read and write is to take away the other aspects of the learning experience. In other words, show them what they already know and let them figure out for themselves how to move beyond it.Another advantage to hiring a tutor is that they can help you find what you're trying to do and help you put it into words. Again, this is a hard skill to learn and is one of the main reasons people fail. If you teach someone how to turn thoughts into words, and then they don't know what they want to say next, chances are, they won't even finish the thought.When you're teaching somebody how to write, all they have to do is watch you. You don't have to do much of the work - they can sit there and listen, and that's all they need to hear. You can ask them questions, but other than that, you have nothing to do to make them understand what you're saying.Writing isn't hard, but learning how to use the tools that exist to write doesn't come naturally to some people. Most of the time, it doesn't come easy either. This is why it's nice to hire a writing tutor who can work with you, teach you new things, and help you use your writing to get what you want out of it.

Spirtual Life Coaching

Spirtual Life Coaching What is a Spiritual Life Coach? ChaptersTaking Control Of Your LifeHelp When You’re Feeling StuckTrusting Your CoachNot Just a Regular Life CoachMeditation and Mindfulness  Spiritual HealingA spiritual life coach is a coach that helps you change your life by changing the way you operate on a deeper level. Rather than just examining your behaviours, habits, and goals, they delve into your deep-rooted beliefs to help you improve your life.  Understanding yourself and the world around you from a spiritual perspective can help you lead a more meaningful life or can just give you a different perspective on life so you can achieve your goals or solve problems in your life. looking for a way to connect with themselves on a deeper level. This is where a spiritual life coach comes in.The roles that a spiritual life coach take on can be very different from those of a standard life coach. A spiritual life coach can walk you through an entirely different set of goals such as exploring different methods of spirituality like healing, or meditation. These goals aren’t always easily defined or measured, and they present a whole new task for life coaches. A regular life coach will help you achieve and move forward in life, but they may not help you get the spiritual fulfilment that you are looking for. Spiritual life coaches, however, are experienced with helping people find their sense of peace and purpose, as well as an appreciation for what you already have in life.Most importantly, a spiritual life coach can help you learn to trust yourself and your intuition. They will show you how to trust your own instincts in making decisions in life.  Meditation has so many wonderful physical and mental health benefits. (Source: Pixabay)Meditation and MindfulnessMindfulness and meditation have become increasingly popular in recent years as ways to deal with stress and to help centre ourselves in our busy lives. Meditation is also known to improve brain function, sharpen intuition, and allows you to reset your m ind and get a fresh start. Most spiritual life coaches are familiar with meditation, and they often suggest meditating to clients to help them connect with themselves and to help clear their minds. Many people use a spiritual life coach to get better in touch with themselves. They can help you connect with a deeper meaning of the world and of life in general. They work on helping you find a balance so that you and those around you can benefit and thrive just by doing the things that you love every day.  Spiritual HealingSpiritual life coaches work with their clients to create new habits and integrate beliefs that are designed to take us where we want to be in life. Healing is often used as method to leave the past behind and focus on the future. For many, healing is the fastest way to ensure a full transformation of mind, body, and soul.There are many different methods used by spiritual life coaches and healers. Spiritual life coaches may be trained in one or several different techn iques. These methods can range from ancient rituals to very modern practices and can be vastly different from one another. You can try several techniques or practices to see which you like best as well as to see which methods are most effective. A spiritual life coach can act as a guide along the path to healing and help you figure out which methods best suit your needs.Chakra HealingChakras are thought to be the energetic centres throughout our bodies that correspond with our emotions and vital health areas. Many believe that blockages of these chakras can lead to illness, stress, as well as mental and emotional problems. If this is something that sounds familiar to you, talk to a coach about chakra healing to help improve your wellbeing. ReikiReiki healing boosts energy levels throughout the body with a hands-on technique. According to Reiki practitioners, energy is what gives us life. So Reiki practitioners work to bring thriving energy to the ailing parts of the body in order to restore balance.Crystal HealingCrystal healing is often used in conjunction with chakra healing. It focuses on specific chakra related centres of the body. Crystal healers believe that crystals possess healing energy and that different types of crystals serve to cure various illnesses and disorders. Some spiritual life coaches may be experienced with this practice and should be able to help you find peace and balance with your own crystal collection.Even if you’re not dealing with a crisis in your life right now, everyone could benefit from spiritual coaching. It can help all of us find different perspectives and help us lead happier, more fulfilling lives!Want to know more about coaching? Check out these sessions that can help with various areas of your personal and professional life:personal development coachingcreative coachinghealth coachingbusiness coaching

How to know you should turn down a job offer - Introvert Whisperer

Introvert Whisperer / How to know you should turn down a job offer - Introvert Whisperer How to know you should turn down a job offer Turning down a job offer sounds preposterous to a lot of people. It is usually the last thing anyone would ever want to do, but there are times when turning down a job offer is the best thing to do for yourself. After months of applying and working on your job search, an offer is the expected end, but sometimes the offer you end up getting is far worse than you expected. Unfortunately, some job offers just shouldn’t be accepted. If you are waffling about accepting an offer, this information can help you. Here are some factors to consider when deciding to leave a job offer on the table. It’s the wrong rung on the corporate ladder. If you are looking to climb the corporate ladder, accepting a position that doesn’t help you attain your career goals is the wrong decision. Settling for just any job is not the solution, unless you really need to start making some money. If you are not in dire straits, you have the opportunity to say no when the job you are offered doesn’t align with your lifelong career goals. It’s just a bad fit. If you applied for a job and later found out during the interview process that the corporate culture does not align with your belief systems, then definitely say no. If you don’t feel that you would fit in, this is the first sign of a future of unhappiness in that position. Sometimes a paycheck and great benefits are not worth your morale and happiness. Although you may be scraping by without a paycheck, you would be better off unemployed than employed by a company that you hate working for. You’ll work too many hours. If your family life will suffer because you will be working too many hours per week, just say no to the job offer. The work-life balance is important than experiencing burnout from working too much. Your personal life is too important to sacrifice for a paycheck that doesn’t begin to compensate missing important family functions. Working too many hours also leads to both physical and mental health problems. Working more than 50 hours per week is not worth the detrimental impact on your health. You’re already looking for your next job. If you are considering accepting this offer while planning to search for a better job, do everyone a favor and decline the offer. Using valuable time working at a job that you don’t want to be working at is disheartening. It is likely if you accept the job you were offered that you will be fighting the urge to quit the whole time and soon end up back where you startedâ€"in unemployment. Gracefully exit by politely refusing the offer before you walk off the job in a huff dissatisfied. It doesn’t pay enough. If the job is great but the pay is not, you may decide to say no while you weigh your options for a higher paying job. However, if the only reason you are attracted to the job is the paycheck, decline it â€" again, unless you are desperate for a paycheck. Spending valuable hours of your life at a job that you hate just to rake in a top salary will make you miserable because money is not enough of an incentive to counteract the misery. If you are leaving your current job for a higher paying job, be sure that you won’t be losing valuable benefits at the job that you already have. Calculate everything including the new commute before you make the decision based on a pay increase. You see better opportunities elsewhere.   If you’re on the fence, one last look around won’t hurt. Before you decide to accept revisit the job resources you used. If you haven’t already, check in on industry-specific and location-specific job sites. Often, opportunities here are not posted on the bigger search sites, and you may have missed them the first time around. There’s a high turnover rate. If a workplace has a high turnover rate of employees voluntarily leaving for reasons other than retirement, there are probably negative things causing them to leave. It could be boredom, low pay, or bad bosses that cause employees to terminate their ties with an employer. You need to investigate and find out why there is a revolving door problem there. If a number of employees are leaving frequently, follow their lead and just say no without the interim stint as an employee. You’re envisioning a grim future. If you have discovered that the industry is a sinking ship, don’t sign on for the beginning of the end with the company. You want to hitch up with a company that has a bright future rather than one with the heyday in the past. Make sure you calculate the risk of a layoff if a merger is in the works. There is nothing worse than being the last one hired and the first one fired. If you make the final decision to walk away, then you know what to do next. You continue the job search until you find the best opportunity for you.

Online exponent properties Tutors

Online exponent properties Tutors Exponents is the power or degree to a given variable or number. The exponent can be any real number. There are many different properties of the exponents in algebra which help in solving many types of question having exponents. Mentioned below are some properties of exponents. Multiplication rule: am * an = a(m+n) (Here the base is the same value a) Division rule: am / an = a(m-n) (Here the base is the same value a) Power of a power: (am)n = amn Example 1: Find the value of x in the equation 3(x+2) = 27. Solution: Here the given equation is 3(x+2) = 27. We need to simplify the 27 further. The number 27 can be written as 27 = 3* 3 * 3 So, 27 = 33 Now we get 3(x+2) = 33. Since the base number is 3 we can equate the exponents. X + 2 = 3 (subtracting 2 on both sides.) X = 3 2. Hence the value of x = 1. Example 2: Find the x in the equation 102 = 1/100. Solution: Here the given equation is 102 = 1/100. The fraction, 1/100 = 100-1. We need to simplify 100 here further. The number 100 can be written as 100 = 10* 10 So, 100 = 102 Now we get 10(x) = (102)-1. Using the power of power rule. 10(x) = (10-2) Since the base number is 10 we can equate the exponents. Hence the value of x = -2.

A Student Review of University of California-Berkeley

A Student Review of University of California-Berkeley The tutors behind Varsity Tutors are not just here to teach theyre sharing their college experiences as well. Aakash is a San Francisco-Bay Area tutor and 2013 graduate of University of California-Berkeley. He holds a Bachelors degree in Public Health and Psychology and tutors several subjects, specializing inAlgebra tutoring, Geometry tutoring, and Physics tutoring. Check out what Aakash had to say about his time at University of California-Berkeley: VT: Describe the campus setting and transportation options.How urban or safe is the campus?Are there buses or do you need a car/bike? Aakash: University of California-Berkeleys campus is rich, in all senses of the word with various extracurricular opportunities and countless classes, spans of green grass and nature, and some of the best food! I would describe the campus as more urban than rural. While there is a lot to do in the city of Berkeley, as with most places, there are places that a student should avoid at night for safety reasons. VT: How available are the professors, academic advisers, and teaching assistants? Aakash:In my experience, teaching assistants are almost always available to meet and help you whenever you are stuck on an assignment or are having a difficult time in class. However, with academic advisers and professors, it varies. Some professors tell you to email them to set up an appointment, while others hold regular office hours. With academic advisers, it really depends on what your major is and what college you are in. The larger colleges, such as the College of Letters Science, do usually have a long wait to meet with academic advisers. If you are in a smaller college, the wait is sometimes shorter. If you have already declared your major, it is usually easier to meet with your academic adviser. VT: How would you describe the dorm life rooms, dining options, location, socialization opportunities with other students? Aakash:The dorm life was awesome! It was a great way to meet new people and make many new friends beginning in freshman year. While the rooms are pretty small at University of California-Berkeley, it was not that much of a problem, considering that you are always out and about somewhere. The dining options varied depending on the place you went to eat and the time of day, but there are always great options throughout the city. Since a lot of people live together in a dorm, it is very easy to socialize and interact with other students. Even outside the dorm (through extracurricular activities like clubs and organizations), University of California-Berkeley is very friendly. VT: Which majors/programs are best represented and supported?What did you study and why? Did the university do a good job supporting your particular area of study? Aakash:Some majors that I think are best represented and supported are Engineering, Business, and Computer Science. I decided to study Public Health and Psychology, while also taking the prerequisite courses to apply to medical school. I was interested in the preventative, upstream approach of medicine, while also concerned with how behavior and cognition influence it. I found that the university did a good job in supporting my particular area of study, and it provided me with a strong foundation to build on both inside and outside of the classroom. VT: How easy or difficult was it for you to meet people and make friends as a freshman? Does Greek life play a significant role in the campus social life? Aakash:Given the closeness of the dorms and the various Welcome Week activities, I would say that it was very easy for me to meet people and make friends as a freshman. Some of my closest friends to this day are people who I had the opportunity to meet during my freshman year. Greek life plays a significant role in the campus social life. Over 80% of students are involved in some type of fraternity or sorority. VT: How helpful is the Career Centerand other student support services?Do many reputable companies recruit on campus? Aakash:I utilized the Career Center once to look over my resume and to help with writing my medical school personal statement. Although I never attended the job fairs on campus, I know that many reputable companies come out to recruit students for internships and post-graduate jobs. VT: How are the various study areas such aslibraries, the student union, and dorm lounges? Are they over-crowded, easily available, spacious? Aakash:It varies. Libraries get very crowded during dead week. However, throughout the year, space is available. When libraries get crowded, there are also other spaces within other buildings for students to study in. Dorm lounges are usually spacious and easily accessible, but they are not always the quietest study locations. The campus also has many cafes with lots of space (and free wifi) for students to study in. The same is true of the city. VT: Describe the surrounding town. What kinds of outside establishments / things to do are there that make it fun, boring, or somewhere in between?To what extent do students go to the downtown area of the city versus staying near campus? Aakash:The campus is situated in the heart of the city of Berkeley. Many great restaurants, bars, and parks/trails are a short walk or bike ride away. Berkeley is also conveniently located a bus ride away from Oakland and a BART ride away from San Francisco. This makes it easy to get away if you are getting tired of campus. My friends and I have definitely gone to the city on Friday nights to get away. VT: How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Aakash:The student body is fairly large, and the typical class size can vary depending on the course. If it is a class that everyone wants to take, it can get to be about 700 people! However, we always have discussion groups of about 20-25 people, which allow for individuals to share and discuss the course content, as well as go over material in a smaller setting. While it is easy to get lost in the sheer numbers of the university, the large volume presents countless opportunities for work, study, and fun. VT: Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one youregretthe most. Aakash:To fulfill an Arts and Literature requirement, I signed up for a Music of India course. Not knowing what to expect, I showed up to class on the first day and learned that we would be critically analyzing classical Indian music throughout the term. With no musical background, I was terrified. I spoke with the professor, and she assured me that no experience was necessary and that it would be a fun way for both of us to learn something more about music. I took her advice and decided to stick with the class. Fortunately, I thoroughly enjoyed the class, and she quickly became one of my favorite professors in college. It was particularly fun working with her to write my final paper in the course, which analyzed the similarities between modern electronic music and traditional Indian classical music. Check out Aakash's tutoring profile. The views expressed in this article do not necessarily represent the views of Varsity Tutors.

The Best Online Resources to Review the Concepts of Physics

The Best Online Resources to Review the Concepts of Physics Online Physics Revision Resources ChaptersThe Most Noteworthy Applications to Acquire the Fundamentals of PhysicsBest Podcasts to Learn More About PhysicsInstrumental Tips to Successfully Revise Physics“Teachers need to integrate technology seamlessly into the curriculum instead of viewing it as an add-on, an afterthought, or an event.”  -  Heidi-Hayes JacobsWe are currently living in the 21st century (in case you  were living under a rock and hadn't been advised), and our teaching and learning methods need to reflect this fact.Educators have the immense responsibility  of encouraging pupils to implement technology to acquire new academic concepts. We cannot be ignorant and continue to use archaic methods in the classroom; the youth of today seem to born with electronic devices in their hands and respond positively to e-learning.Websites, e-books, applications and podcasts can all be utilised in the classroom and afterwards to complete homework assignments.  Since we are living in the information age, the interne t has plenty of options to ensure student success in a wide variety of academic disciplines. However, the primary issue  seems to be the overabundance of educational alternatives making it challenging to find an option that suits your unique learning style.Have no fear Superprof is here!We have searched the internet far and wide to find the most highly recommended mobile phone applications and podcasts to master the fundamentals of physics inside and outside the classroom.And what would an article about reviewing physics be without some useful suggestions? Therefore, you guessed it, some additional tips from qualified experts about how to adequately consider the concepts of physics have been provided in this article to make the experience of studying physics something beneficial and enjoyable.There are a wide variety of educational applications available for download on the primary application stores that help individuals learn a new language, a foreign concept or more about an acad emic discipline.We will analyse some of the most highly recommended applications that are essential in grasping the basic concepts of physics.Online learning is not enough? Hire a  math and physics tutor.Khan AcademyThe Khan Academy is a non-profit organisation that seeks to instruct all interested ones about any academic discipline that may be of interest. Khan Academy's mobile app allows students to learn more about anything on the go.There are plenty of videos and articles that help students learn more about the basics of physics. There are also practise questions that include step by step hints to ensure success. The application even features offline access to valuable information about physics to keep learning while on your commute to work or school.The application is completely free, extremely educational, and highly recommended for students wanting to learn more about physics from all ages.  Pocket PhysicsA fantastic application to have at your disposal that purely focuses on learning more about physics. The app is 100% free and concentrates only on the key topics that are necessary to succeed.All critical concepts, equations and formulas of physics are included to help students refresh their knowledge after class or prepare for an upcoming examination.Considered by many as the best app about physics available on the Android market. Essential topics of the physical world include linear motion, force, gravity, waves, elasticity, electricity, thermodynamics and astronomy.Android users would be wise to use the Pockets Physics application daily to excel in physics throughout the school year. Remember small study periods every day are better than an afternoon of reviewing once a week.PhyWiz Physics- Physics SolverA helpful application to aid struggling students with their homework. There is step by step questions for over 30 physics topics such as forces, gravity and quantum physics to name a few.The application has a 4.6 out of 5 rating on the Google Play S tore and offers key features that users adore such as the ability to help solve problems quickly and logically, over 100 equations at your fingertips and the option to ask any physics question and get an answer instantly.High School PhysicsAre you in secondary school and needing help with physics? The solution is the High School Physics application that covers many essential topics offering simple definitions about concepts from the physical world.Some pupils claim that physics is too hard because there are too much maths used in physics. Therefore, the developers of the High School Physics application have thought about this concern and created a great tool that permits students to concentrate on physics without becoming discouraged by the heaping amount of mathematical equations.If you prefer to use physics revision books than applications, check out Superprof's article about the most highly recommended books to use when reviewing physics.Best Podcasts to Learn More About PhysicsP odcasts have helped everyday people learn more about academic concepts. (Source: pixabay)Podcasting has become increasingly popular in recent years; it is a free service that allows listeners to download audio files from podcasting websites to listen to them on their personal computers or digital audio players. The term is a combination of the words iPod and Broadcasting.Podcasting started to became readily used and relevant in 2004 and a wide variety of categories can be listened to such as arts, beauty, business, comedy, health, hobbies, music and education.  Podcasts are a fantastic tool for persons who want to learn new things on their commute to work, while taking a walk or while exercising.  To meet the demands of individuals interested in the basic concepts from the physical world, there have been various podcasts developed that touch on essential topics of physics. Without further ado, we will now consider some of the most highly recommended podcasts covering the fundamental s of physics.The Titanium Physicists PodcastDr Ben Tippett and his team believe that anyone can understand physics. Complex physical concepts are explained used fun metaphors, explanations and experiments.There are over 70 episodes that can be download and listened to at a time most convenient for you.Visit their website to subscribe and listen to there scientific podcasts on a regular basis.Khan Academy PhysicsA fantastic educational podcast that should be subscribed to immediately! There are 117 episodes available on the iTunes Podcasts store. Episodes usually last 9-10 minutes and discuss essential physics topics such as magnetism, fluids, motion, Newton's laws and thermodynamics.This well-developed podcast from Khan Academy is a perfect solution for students struggling with physics and have a tight schedule. A physics podcast a day keeps the bad grades away!Physics by Yale UniversityWant a taste of Ivy League education on your way to work? Look no further, the extremely informat ive physics podcast developed by Yale University features professors, lecturers and distinguished speakers discussing physics, quantum mechanics, and the mysteries of the universe.If an educational lecture in physics in American English doesn't bother you, there are six podcasts available on the iTunes Podcast store that range from eight to ten minutes in length. Physics topics such as dark energy and the force of light are reviewed by experts.Physics from the Imperial College LondonThe Imperial College London is a world-class university that delivers excellence in a wide variety of academic disciplines and physics is no different. Their physics podcast is informative and comes highly recommended.According to the iTunes Podcast Store, 79 podcasts are varied in length and perfect for reviewing some essential physics topics.Instrumental Tips to Successfully Revise PhysicsSince physics, along with chemistry and biology, is one of the most challenging academic disciplines studied by pup ils during secondary school and university, helpful tips are always welcomed with open arms to ensure success.To succeed in physics effective study strategies are needed.  Without further ado, the following are some of the most beneficial suggestions to revise physics and ace exams successfully:Think Conceptually:  the academic discipline is unlike other subjects such as history and language arts where memorisation is essential for  success. When studying physics, pupils need to use big-picture conceptually thinking. The basics need to be correctly understood before moving onto more complex concepts. Having a conceptual approach aids students to break down problems into simple steps. Remember, Rome was not built in a day; it was made brick by brick or stone by stone. The same is true with physics; working through the small steps will effectively help students to solve more massive physical problems,Have a Study Schedule:  turn your phone off, find a quiet place and avoid extrinsic d istractions. By finding a quiet area, studying physics will become more productive. If you're using a recommended site to review physics, make sure email notifications and other distracting things are turned off. Remember that scheduling a few minutes each day to review physics is essential for academic victory,Develop a Love for Maths:  it is proven that students excel on subjects they enjoy. Therefore, develop an appreciation for mathematics since it is a prerequisite for success in physics. Viewing mathematical equations as a painful chore will only make matters worse and discourage you from developing your maths skills. If you are having trouble motivating yourself in math class, hire a dynamic private tutor to cover the necessary basics of algebra, trigonometry, and calculus.Reviewing physics does not have to be a traumatising experience. With the help of modern-day learning tools such as podcasts and applications, developing a firm grasp of the fundamental concepts of physics can be done triumphantly!

Area of a Hexagon

Area of a Hexagon Area of a Hexagon Geometry is a branch of Mathematics which deals with studying shapes of various dimensions and analyzing their properties. In this study of shapes, the polygon family is one of the most commonly studied figures. Polygons are closed 2-dimesional flat objects which have straight sides. The polygon consisting of 6 sides and 6 angles is known as the Hexagon. Any closed flat 2-dimensional structure with 6 straight sides will be referred to as a Hexagon. The word hex means 6 and gon refers to angle. As shown in the diagram below, a hexagon has 6 sides or edges, 6 angles and 6 vertices. Area of a hexagon is the space occupied within the boundaries (or sides) of the hexagon. Using the side and angle measurements, we can find the area of a hexagon. Hexagons can be commonly observed in different forms in our beautiful nature around. The below figure shows us the shaded portion inside the boundaries of the hexagon which is called the Area of a Hexagon. Types of Hexagons: Hexagons are classified primarily into 2 types: Regular Hexagons and Irregular Hexagons. 1) Regular Hexagon: A hexagon which has all of its 6 sides equal in measure is known as the Regular Hexagon. Along with its 6 equal sides, it also has all its 6 angles equal in measure. Therefore when a regular hexagon is divided into triangles by joining its diagonals, 6 equilateral triangles are formed as shown in the figure below. (Note: Diagonal is a line segment formed by joining any two non-adjacent vertices as shown in the figure on the right). Area of a regular hexagon can be easily calculated by considering the 6 equilateral triangles formed inside. 2) Irregular Hexagon: A hexagon which does not have 6 equal sides is known as the Irregular Hexagon. This type of hexagon does not have 6 equal angles as well. If the vertices of an irregular hexagon point outward, then it is known as a Convex Irregular Hexagon, and if the hexagons vertices (or at least 1 vertex) points inward, then it is known as a Concave Irregular Hexagon as shown in the figure below. Since the sides and angles measurements are unequal, hence we have to use different strategies to find the area of an irregular hexagon. Area of a Hexagon: Area of a hexagon is the space occupied by within the sides of the hexagon. The method to calculate area of a regular hexagon differs from the method to calculate the area of an irregular hexagon. Area of a Regular Hexagon: A regular hexagon has all the 6 sides and 6 angles equal in measure. When diagonals passing through the center of the hexagon are drawn, 6 equilateral triangles of equal size are formed (as shown in the figure below). If the area of one equilateral triangle is calculated then we can easily calculate the area of the given regular hexagon. If a convex regular polygon has n sides, then the sum of all its interior angles, S = (n 2) * 180 Therefore, sum of all the interior angles of a convex regular hexagon S = (6 2) * 180 = 720 If a convex regular polygon has n sides, then Each Interior angle = (n 2)/ n * 180 Therefore, each interior angle of a convex regular hexagon = (6 2)/6 * 180 = 120 Given a regular convex hexagon as shown in the figure above, where point C is the center of the hexagon. Triangle ABC is an equilateral triangle, as all the angles inside triangle ABC are equal to 60 (half of the interior angle 120). Hence all its sides are also equal. Therefore, let the side lengths of AB = BC = CA = s CM is the perpendicular drawn to the side AB. Let CM = h As M becomes the midpoint of side AB, hence MB = s/2 (half of the side length of AB). Now in triangle CMB, 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 ABC , h = s* 3/2 Now, Area of triangle ABC = 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 ABC = 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 8cm? Given that the side length, s = 8cm Area of a regular hexagon, A = 3/2 * s2 * 3 Hence, Area = 3/2 * 82 * 3 = 963 which is 166.3cm2 (approximately) Example 2: If the area of a regular hexagon is 12 square feet, then what is the side length of the hexagon? Given Area of a regular hexagon, A = 12 square feet and this can be further simplified as 23 ft2. Area of a regular hexagon, A = 3/2 * s2 * 3. Therefore, 3/2 * s2 * 3 = 12. This implies s2 = 2/3 * 12/3. This gives: s2 = 2/3 * 23/3 (123 can be also written as 23). Hence, s2 = 4/3. This implies s = (4/3) = 2/3 = 1.15 (approximately) Therefore, the side length of the regular hexagon is 1.15ft (approximately) Area of an Irregular Hexagon: Finding the area of an irregular hexagon is not the same as finding the area of a regular hexagon. Area of a regular hexagon can be easily calculated using the formula we have above, but for an irregular hexagon we use various methods according to the given information to find its area. Let us look at an example below where the information is given in the figure. 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 = (10+ 6 + 10)/2 == s = 13 Now Area of triangle A = [s(s-a)(s-b)(s-c)] = [(13* (13 -10) * (13 6) * (13 -10)] Area of Triangle A = (13 * 3 * 7 * 3) = 28.6m2 Triangle B: s = (10 + 11 + 7)/2 = 14 Area of triangle B = [(14 * (14 10) * (14 7) * (14 11)] = (14 * 4 * 7 * 3) = 34.3m2 Similarly using Herons Formula as shown above, we get the areas of triangles C and D as well. Area of Triangle C = 16.9m2 and Area of Triangle D = 19.9m2 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 = 28.6 + 34.3 + 16.9 + 19.9 = 99.7m2 Perimeter of a Hexagon: Perimeter of a hexagon (regular or irregular) can be easily calculated by adding all the side lengths of the given hexagon. Perimeter of a Regular Hexagon is equal to sum of all its side lengths. Therefore, Perimeter of a Regular Hexagon of side length s (as shown in the figure on the right) = s + s + s + s + s + s This gives us Perimeter of Regular Hexagon = 6s Perimeter of an Irregular Hexagon is also sum of all its side lengths. If a, b, c, d, e, and f are the side lengths of an irregular hexagon (as shown in the figure on the right),then Perimeter of an Irregular Hexagon = a + b + c + d + e + f