Biology 110

Biology 110Biology 110 is the most popular and in demand course offered by the University of Texas. This course, as the name suggests, deals with the study of life sciences and all their application.The idea behind offering this course was to bring in more students and take the chance of introducing a new course. After a lot of attention on the good results achieved by Biology 105 and 106, the Vice-Chancellor of the University decided to offer a new subject. Biology 110 focuses more on the study of life processes and how they are controlled. The physical features of organisms, the body mechanics, cell biology, nutrition, the genetic mechanisms are all important factors for understanding life processes.This Department Offering is a 'must' for anyone who wants to pursue the study of biology in a research university. This subject has been rated very highly by most biology students and even more so by the academics who are involved in the preparation of the syllabus. It is an area of spe cialization for which there is a lot of emphasis in the faculty members.This course introduces you to the study of various aspects of genetics, cell biology, systems biology, the genome, and developmental biology. All these subjects are crucial to comprehending the vital importance of each element in the study of life sciences.You will learn about the evolution of life by examining the major topics in evolution, the biological basis of life, biodiversity, and animal husbandry. You will also learn about the way living things adapt to the environment by studying the physical features of animals, living systems, and different organisms. Physics will be taught in the Biology 110 as it deals with the study of living systems and their reactions to the environment.You will learn about the functions of an organism and how they control the development of the whole living system. The nervous system and the brain are two important elements in biology. Onceyou have mastered these two aspects of life, you will be able to understand the purpose of all these study areas.There are many reasons why the course is so popular. For one, the degree course in Biology 110 is almost equivalent to that of a graduate level course in the Life Sciences. You will also get a good grounding for your career in the area of Biology. In addition, this course also gives you a chance to participate in world class research.

What Is The BSA Chemistry Merit Badge?

What Is The BSA Chemistry Merit Badge?If you have not heard of the BSA Chemistry merit badge, it is a kind of educational certification for students who would like to pursue a career in chemistry. The badge is aimed at creating better chemistry education in schools, in order to make chemistry more familiar and acceptable to the younger generation. Today, students can get it at the school level, while at some point of time in the future, they will be required to go through college to become a chemist.One of the types of science, which is very popular with people of all ages is chemistry. Science and art have always been a source of interest for many young people. It helps to see how well these two things can complement each other and how well their interests and enthusiasm can affect their grades.The BSA Chemistry merit badge is a product of the National Council for Science and Mathematics (NCSM). This can only be obtained after one has successfully passed the national entrance exams in chemistry. After passing the national examination, one can enroll in a college or university to pursue a degree in chemistry.In order to earn the BSA Chemistry merit badge, one should do well in a course in chemistry. At first, the course may require a lot of hard work and dedication. Students who are not able to do well in their classes would be ineligible for the badge. Those who already have a diploma in chemistry can enroll to go for the next level, which is Chemistry B, and take up a job in industry.Chemistry is considered as one of the fields which can help to understand everything in the world around us. It also allows the chemistry to be applied in other sciences. It has become increasingly important to study this field because it helps scientists understand what they are doing. People who love science would also love chemistry.Science and engineering also benefit a lot from studies on this field. They will also learn about many of the molecules in nature, its properties and its processes. With today's technology, there are many instances in which we need the help of scientists. The BSA Chemistry merit badge helps to encourage and reward students who love this field of study.There are many other ways in which the BSA Chemistry merit badge can be earned. These include a thesis which is meant to represent the progress of a student in a certain topic, while at the same time providing a test for every student who wants to earn it. Aside from the above mentioned ways, there are a lot of ways that can help students who want to go through a certain degree.

How to Prepare for a Singing Audition Ten Tips for Success

How to Prepare for a Singing Audition Ten Tips for Success Sign up successful Preparing Your Music, Part One  â€" If youre auditioning for a rock band, selecting a pop ballad for your audition song probably wont fly.  By the same token, if you’re auditioning for a music theater or opera role where the character has great emotional depth, rather than showing the panel you’re versatile, a light and fun piece will simply show them you don’t understand how to prepare for a singing audition, or worse still, you’re not familiar with the plot!  For stage auditions, you’ve most likely been given something from the show to present to the panel.  How you prepare this is essential to your success. Preparing Your Music, Part Two  â€" If you play the piano well enough even to pick out a tune line, you can familiarize yourself with the melody of something new to you very quickly.  Identify the bars you’ll have trouble with, and work out exercises based on those bars that will help you conquer them.  Don’t worry about memorizing your words just yet, but make sure that the melody is really part of you, practicing on a variety of vowel sounds.  Read through the text of your song or aria as a piece of prose or poetry, and note how you naturally color the words when you say them.  Go back to your melody, sing through it on the vowel sounds of the words, and then gradually add the text.  You’ll find that the memorization process is much easier this way. Preparing Yourself â€" One of the hidden factors of how to prepare for a singing audition is the unsavory truth is that its a visual business.  Make yourself the best version of you that you can be â€" clean and pressed clothes, clean shoes, and a high level of attention to personal grooming will all make the audition panel see that you take the job (and more importantly, yourself) very seriously.  In the longer-term, pay attention to diet and physical fitness; even if you are carrying extra pounds, fit and healthy shows in the way you move and present yourself. The Day Before â€" Often overlooked in how to prepare for a singing audition is factoring in fun!  Aim to be so well prepared that you don’t need the day for extra preparation (unless the audition was a very short notice surprise!); spend that day in the beauty salon, walking in the park, or meeting friends for lunch to clear your brain ahead of the pressures of the audition room. The Day Itself â€" Get up early, and certainly no later than three hours before the time you have to sing.  Remember that your voice takes longer to wake up than you do!  Lay out your clothes and music the night to say time and double-check that you have everything you need.  Take advantage of the steam in the shower, and do your warm up then there may not be time or space at the venue. Also, make sure you leave extra time for traveling and finding exactly where you need to be, especially if youre not familiar with the venue. Being Professional â€" Another unsavory truth as you get further on in the profession is that other singers may do all they can to psych you out in the waiting room.  Don’t engage with this behavior, and certainly don’t be put off by tales of how they’ve done the role before for X or Y company, or how they had dinner with the director only last week.  Factor in being calm and collected as part of how to prepare for a singing audition.  Make sure you have copies of your resume and headshots with you, and don’t forget to check your schedule for any clashes with the rehearsals! Saying Thank You â€" If you feel you’ve done poorly, you may want to run out of the room as quickly as you can, but don’t be tempted to leave without a word.  Thank the panel for their time, and even by email afterward especially if their response has been positive! Picture it like this: two sopranos are auditioning for the same role.  One is a little better than the other, and while very reliable, musical, and well-prepared, has a reputation for being a little difficult.  The weaker singer, however, has a reputation for always turning up on time, prepared to throw themselves in to any extra jobs that need doing, and able to get along well with their colleagues. Who do you think gets the job? Conclusion You may be the most self-reliant and talented singer in terms of how to prepare for a singing audition.  However, without a trusted pair of ears to pick up on any bad habits you may not be aware of, your progress may stall. Singing lessons with a qualified teacher are essential at every level -not just to learn new vocal techniques, but to strengthen and revisit existing ones.  A good teacher is an essential investment in your enjoyment of singing, whether you’re an enthusiastic amateur, an aspiring student, or an established professional.  Even famous singers like Pavarotti and Sinatra took voice lessons what’s your excuse? Interested in Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher  Photo  by U.S. Army

5 Best Apps for College Students

5 Best Apps for College Students Jill Cole Being a college student in 2014 has its pros and cons. The competition is fierce and college courses are more challenging and demanding. However, coupled with these expectations come a ton of technological tools and apps that can help make your life easier and more efficient. Here, tutor Natalie S. has picked out a few of the  top apps for college students that you should download right now! 1.  Dropbox This app and desktop tool enables you to back up all of your documents and easily share them with others. You’ll never struggle with emailing large attachments again, and you’ll never have to worry about losing all of your documents if your computer crashes. You can download Dropbox to your desktop, so you can save all of your files to this location instead of on your computer. Then, all of the info in your Dropbox syncs to the cloud and when you log into your account online, the account mirrors whatever you have saved on your desktop Dropbox. If you’re responsible for a group project, you can create a Dropbox folder and invite all of your group members to join. You can save all documents there and any updates will be seen in real time. 2.  Mathway This app is a great tool for students who are not mathematically inclined and who need additional help navigating homework and prepping for exams. You can utilize the Mathway app to check many math concepts, including your algebra, geometry, or calculus math homework. Also, if you’re stumped on a problem, Mathway will show you step by step how it can be solved. 3.  iTunes U This is a fantastic app to use in conjunction with your class lecture notes. iTunes U features lectures on all subjects by professors from leading universities, including as Cambridge and Yale. You can download lectures that correspond to the subjects you’re studying, and use iTunes U to supplement your lecture notes  and in-class seminars. 4.  SelfControl This app is designed to block certain websites like Facebook, Twitter, and other social media sites that take your attention while you’re studying. Just download the app and tweak the settings, so you can block specific websites for a specific amount of time. Once you finish studying, SelfControl will turn off, and you will gain access to your favorite time-consuming social media sites once again. 5.  EasyBib This app is designed to help you correctly format all of your sources, so you can easily create your bibliography page for your research papers. Formatting bibliographies can be a daunting, time-consuming challenge. This app helps you create citations in multiple different styles, including MLA and Chicago. All you have to do is either search for the book or article you want to cite, or enter the basic information manually, and EasyBib will instantly create the correct citation. Whether you’re struggling with citations, self-control, math or file sharing, these apps for college students are must-haves to download right now! Natalie S. tutors English, ESL, History, Phonics, Reading, and  Test Prep in San Diego, as well as through online lessons. She received her BA in English Education at the University of Delaware, and her MA in English Literature at San Diego State University.  Learn more about Natalie here! Interested in Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher Photo by  IN 30 MINUTES Guides

What is it Like to Attend St. Marys University

What is it Like to Attend St. Mary's University The tutors behind Varsity Tutors are not just here to teach theyre sharing their college experiences as well. Christine is a Houston tutor and 2012 graduate of St. Marys University in San Antonio, Texas. She holds a Bachelors degree in Biology and currently specializes inmany subjects including Algebra tutoring, Chemistry tutoring, and Writing tutoring. See what she had to say about her school: 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? Christine: St. Marys entire campus is gated and there are police in cars and on bikes patrolling 24/7. After midnight, all of the gates on campus are closed except one. I have always felt very safe on campus and it is easy to get in contact with the police if you have any safety concerns or need someone to walk with you late at night. Yes, occasionally, there have been cars that do get broken into just like at any parking areas but as long as you do not leave your valuables in sight, your car is unlikely to get broken into. Because the campus is relatively small, a bike is not necessary. On average, it takes about 10-12 minutes to talk from most of the dorms to the classrooms. I would suggest having a car if you need to get off campus often. Another option is riding on the public VIA bus to get off campus. There is a VIA bus stop right by the school. VT: How available are the professors, academic advisers, and teaching assistants? Christine: This is what I loved about St. Marys University the most. My professors and academic advisers are not only my mentors but also my friends. Because most of the classes have about 20-30 students, professors quickly learn each students name. It is easy to meet with professors before or after class and they respond to emails fast. I could also easily meet with them in their office even outside their office hours. You even find students having lunch with their professors around campus. VT: How would you describe the dorm life rooms, dining options, location, socialization opportunities with other students? Christine: St. Marys recently decided to accept more students than they could house. Within the past few years, many students find themselves having 2 roommates instead of the traditional 1 roommate in a bedroom. The school has already started making plans to build more dorm buildings. St. Marys recently changed the dining option to where students buy meals instead of having points. The school also just added Chick-fil-A and Starbucks on campus. I would consider the location of St. Marys to be in a rough area but as I had mentioned, the school is gated and I have never felt unsafe on campus. University Programming Council (UPC) and Student Council do an excellent job with planning school events to ensure that students feel very welcomed and are actively involved in campus life. It is very easy to join several organizations and to make new friends. 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? Christine: There is a large number of Biology majors and Business majors. I was a Biology major and pre-medical student. St. Marys University does an outstanding job supporting Biology majors. All the Biology professors and advisors make sure that the students are on track and assist the students with finding research jobs and applying for professional schools. 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? Christine: I found it very easy to meet people and make friends as a freshman. Most of the students, professors, and faculty are friendly and easy to talk to. While walking to and from classes, students and professors wave and say hi to each other. It is common to see familiar faces when you walk around campus. The warm friendly environment is just part of the Marianist spirit of the school. Yes, Greek life does play a role in the campus social life but I chose not to join a sorority and found myself just as involved with campus life and had just the same amount of friends and fun as sorority girls did. VT: How helpful is the Career Centerand other student support services?Do many reputable companies recruit on campus? Christine: Because I was a Biology major and pre-med student, I did not find myself using the Career Center often because the chair of the Biology department did a superb job of notifying students when and where there were research and clinical opportunities. Throughout the school year, there are a few job fairs and events where companies recruit on campus. The Civic Engagement service does a great job of keeping records of your volunteer work and hours. The only time I went to the Career Center was when I needed help with my resume to apply for a medical school program and for a mock interview. The individuals that work there are very helpful. VT: How are the various study areas such aslibraries, student union, and dorm lounges? Are they over-crowded, easily available, spacious? Christine: I believe it was a good idea for St. Marys to recently remodel the lower floor of the main library to have more group tables and group study rooms. The lower level allows students to talk and use white boards. The second floor has most of the computers and allows students to talk. The top floor is the silent floor. The library does get crowded during finals week, just like most colleges and universities, but most of the time, it was easy for me to find a place to study in the library. Most dorm lounges are good study areas. I would also suggest studying at the Law Schools library, where it is completely silent, if you cannot find any other place to study. 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? Christine: There is not as much to do in San Antonio as compared to the activities in Dallas or Houston. Of course, no student attends St. Marys University for four years without visiting the Alamo and the Riverwalk in downtown at least twice. The La Cantera and Northstar malls are good shopping locations. You will find many delicious Mexican restaurants all over the city. There are a few fun clubs and bars such Cowboys, Wild West, Howl at the Moon, Fox and Hound, and Posh. Most students go to the downtown area or drive at least 15 minutes to go have fun off campus. VT: How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Christine: St. Marys University has a small student body with a total of about 2,460 undergraduate students and a 13:1 student to teacher ratio. I graduated from high school with a class of about 270 students and felt very comfortable at St. Marys. I personally prefer small class sizes where I know almost everyone in the class and can maintain a close relationship with my professors. VT: Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one youregretthe most. Christine: My most memorable experience was being in Dr. Manchesters General Biology class. He has a genuine passion to teach and is extremely knowledgeable. He cares for each of his students and their career goals. Dr. Manchester would teach using a wooden stick that he chopped off a tree outside of the Biology building and he made up funny stories for his students to remember many Biology concepts. His class was by far the hardest class I had ever taken but it was worthwhile because I learned to perfect my study skills in his class. Check out Christines tutoring profile. The views expressed in this article do not necessarily represent the views of Varsity Tutors

Act Practice Test Can Be Easy If You Have TutorPace Beside You

Act Practice Test Can Be Easy If You Have TutorPace Beside You College is one of the most awaited places for many students. Each one craves to reach there and wants to enjoy the freedom and independence that is found there. After the disciplined life of school, it becomes very refreshing to live a college life. Every student wants to attend a good college that will not only provide them with good vision but will also help the vision to get turn into reality. This is only possible when you have got your admission at a reputed and a good college that has good prospects and also good teaching staffs. But thinking of getting admission and reality of getting admission is very different from the other. Getting admission in a good college is very tough but it is very important as well for a better future for any student. Al the reputed colleges have opened up a new way of admitting the students in their colleges and that is through an entrance test. The entrance test is called ACT exam. This is the ticket through which you can be enrolled in any of the good and reputed colleges and universities of most of the nations. As we all need to avail any good college or university for our better future so this exam becomes much more important and it is natural that cracking it will land up a student towards a bright future. ACT and its whereabouts ACT is considered as one of the tough exam through which a student can get admission at a good college of university of the nation. The exam consists of four subjects that are English, social science, mathematics and science. Each exam has to be qualified by the candidate and then only one can get admission in any of the reputed colleges of the town. It is tough to crack al the exams and the entire subject with good percentage. For this you need the help and guidance of a good and eligible teacher who have passed such an exam and can handle the kind of pressure that arrives in. Private teachers are available but there are various students who are unable to take up private tuitions as of many difficulties that they face. The transportation expenses are also high and this makes many students to step back and think of learning and studying at home. When you are thinking about something then you can come and get a try with online tutoring facilities. Today with the advent of technologies various types of inventions have helped us lessen our pressure and work load from our life. Internet is also one such way out. It helps the young generation in various ways and also lands them into various types of information and necessary details that they want. What online tutoring is all about? Online tutoring may seem a new way to learn and teach, but with passage of time this type of learning process is gaining a lot of fan following for itself. The online tutoring process can be said as a way of great stress buster for many students. Many students come up with various problems and this can only be solved with the help of online teachers being beside you. The teachers can carry of various types of subjects with same efficiency and with same approach. The teachers present in such type of online tutoring institutes are very much qualified with a subject and knows how to handle the subject with ease. It is very necessary that one should know the subject properly if they want to teach their students with full proficiency. Online teachers have to go through tremendous tough interview and then only they are appointed. The teachers are known to teach the students well and thus for this they sketch a structured plan and they work over this with ease. The weak areas of the students are detected and then the process of teaching gets started up. This helps the weak students also to rise up and get comfortable with the teacher. The other benefit of online teachers is that each individual student is attended by each individual teacher. This increases the confidence level of students largely and this helps the students to open up with their problems to the teachers and solve them immediately. I have said the word immediately because online tutoring has another major facility and that is the teachers are available all round the clock and also throughout the year. They do not have any holiday and so whenever a student encounters any problem or doubt in any subject they can clear it at that moment from the teacher. Every child in the present timing can easily come up with the knowledge of how to handle internet and how to use it with efficiency. So enrolling oneself in such an institute does not seem to be a great cause of concern as they can for once check the entire process of online tutoring and know what are the basic facts of it and how much is it useful. TutorPace, one of the well known online tutoring institutes In the midst of various online institutes it is very essential that being a responsible parent you should go for such an institute who will guide you, support you and also help you with the subjects that seem to be a nightmare to you. Just for example you can go through the site of TutorPace. It is one of the reputed site that helps in providing you all the above facilities that has been talked about. It has good teachers, throughout the clock service, less charges of any service; individual teachers attend single students and as the entire process of online tutoring are conducted via online chats, tele conferencing, video conferencing, audio medium and so on. This helps in saving time and energy of any student along with also saving god bucks that is generally used as transportation expenses for attending any private tutoring. TutorPace will help you attain Act practice test with its efficient teachers and good features.

Take Your Grades from Good To Great With Online English Tutors

Take Your Grades from Good To Great With Online English Tutors 0SHARESShare The methodology of tutoring is what matters the most Needless to say that English is an international language, and it is necessary for each and every student to get a better understanding of it. This language not only helps you get better grades in English, but enable you to take your grades from good to great in other subjects also. As far as English tutoring is concerned, most parents do not find it very difficult to guide their young ones in this subject. What matters is the tutoring methodology and approach that most parents adopt. A parent may have a very sound knowledge in English, but extending a very good English homework help to kids is totally a different thing. Online English tutors are capable enough of handling students well In the contemporary times, a large number of parents are always engaged in the hustle and bustle of their daily life. It’s almost impossible for them to find time even for observing what the kids are doing. Keeping in view the same, they hire tutors by paying their hard-earned money to them. Here at this juncture, it is very necessary for them to collect some knowledge about the resources of modern tutoring. The online english tutors for English homework help are the best possible solution for English tutoring requirement of kids. When you go online, you have a wide rundown of native tutors who are not only affordable but also have decades of experience in handling kids and the grown-ups. The availability of native online tutors is just a click away As far as effective and result-oriented tutoring is concerned, native tutors can deliver the best results. They are quite natural in their approach, and know it very well how to supply the minutest and subtle grammatical elements to students. The internet has made it possible for you to have an easier access to native online english tutors for English assignment help. [starbox id=admin]

Lateral Area

Lateral Area Lateral Area In geometry, a 3-dimensional figure is the object which has 3 dimensional measurements of length, width and height. Using these 3 measurements, various calculations of volume, surface areas are analyzed. Shapes such as polyhedrons, cylinders, cones and spheres are 3-dimensional figures. Polyhedrons are the shapes which have flat surfaces known as faces, and these faces are made of polygons. Examples of polyhedrons are pyramids and prisms. Cylinders, cones, spheres are 3-dimensional but are not polyhedrons as they do not have flat surfaces. They have curved surfaces. Cylinders have 2 congruent base circles connected by a curved surface. A cone is a figure which has a base circle connected to the vertex on top by a curved surface. A sphere is also one such space figure which has all its points equidistant from the center point. What is Lateral Area? Lateral Area is the sum area of all the surfaces of the figure except the base and the top area. That means, lateral area is the sum of area of all the faces or lateral surfaces only. Based on the shape of the figure, the lateral area can be calculated accordingly. Lateral area is measured in square units. For instance, if the dimensions are in meters, then the unit of lateral area would be square meters. Lateral Area of Geometric Shapes: Lateral area of various geometric shapes can be calculated using the dimensions of that particular shape. For calculating the lateral area, we do not add the areas of the top surface and the bottom surface of the figure. While calculating the Total Surface Area of a figure, we add up the areas of all the surfaces (including the top and the bottom), but for Lateral Area only the areas of the lateral faces need to be added up. Now let us calculate the Lateral Area of various geometric shapes with different sizes: 1) Lateral Area of a Prism: A prism is a very popular 3-dimensional figure which consists of flat faces and identical bases. The bases are congruent and parallel to each other. All along the length, the prisms have the same cross-section. The prism is a polyhedron, so it does not have any curved sides. Its faces are flat and it has edges (or sides) as straight lines. We can classify different types of prisms based on the cross-section or the base of the prism. If the base or the cross-section of a prism is a square, then it is known as a Square Prism. If the cross-section along the length is a triangle, then it is known as a Triangular Prism. Lateral area of any prism can be calculated by using the formula as shown below: Lateral Area of a Prism = (Perimeter of the Base) * (Height of the prism) == L = P * h a) Lateral Area of a Rectangular Prism: A rectangular prism has 6 rectangular faces including the top and the bottom surface. Since the base of the cross-section of the prism is a rectangle, hence it is known as the Rectangular Prism. To calculate the Lateral area of a rectangular prism, we consider only the area of the 4 lateral faces and do not calculate the area of the 2 bases of the prism. The perimeter of the base of a rectangular prism is nothing but the perimeter of the base rectangle. The perimeter of a rectangle is the sum of all its side lengths. This implies Perimeter of a rectangle, P = 2l +2w (where l = length and w = width of the rectangle). Hence the Lateral Area of a Rectangular prism can now also be written as: Lateral Area of a Rectangular Prism = Perimeter of the Base * Height of the Prism L = P * h L = (2l + 2w) * h Or L = 2lh + 2wh (where l = length, w = width, h = height) Example: Calculate the lateral area of a rectangular prism if given that the length is 6m, width is 5m, and height is 8m. Given that length l = 6m, width w = 5m and height, h = 8m. Lateral area of the rectangular prism, L = Perimeter of the base * Height L = 2lh + 2wh == L = (2* 6* 8) + (2* 5 * 8) == L = 96 + 80 = 176m Hence, the Lateral Area, L = 176 square meters. b) Lateral area of a Triangular Prism:A triangular prism is a prism whose base of the prism (or the cross-section along the length) is a triangle. If the sides of the base triangle are a, b and c, then the Perimeter of a triangle is the sum of all its sides = (a + b + c). Lateral Area of a Triangular Prism = (Perimeter of the base triangle) * (Height of the Prism) L = (a + b + c) * h Example: What is the lateral area of a triangular prism whose height is 12cm and which has a base triangle of side length 6cm, 4cm and 5cm? Given height of the prism, h = 12cm The side lengths of the base triangle are a = 6cm, b =4cm and c = 5cm. Lateral Area of a Triangular Prism = (Perimeter of the base triangle) * (Height of the Prism) L = (a + b + c) * h Hence, L = (6cm + 4cm + 5cm) * 12cm == L = 180 square centimeters. c) Lateral area of a Regular Hexagonal Prism:A hexagonal prism is a prism whose base of the prism (or the cross-section along the length) is a hexagon. A hexagon is a polygon with 6 sides. A hexagonal prism consists of 2 identical hexagonal bases and 4 rectangular faces. A regular hexagon is a polygon which has 6 equal sides. If the side length of the base regular hexagon is s, then the perimeter of the base hexagon is the sum of all its sides = s + s + s + s + s + s = 6s. Lateral area of a Hexagonal Prism, L = (Perimeter of the base regular hexagon) * (Height of the Prism) L = (6* s) * h Example: If the height of the prism is 10cm and the base is regular hexagon of side length 4cm, then what is the perimeter of this hexagonal prism? Given height of the prism, h = 10cm The side length of the base regular hexagon, s = 4cm Lateral area of a Hexagonal Prism, L = (Perimeter of the base hexagon) * (Height of the Prism) L = (6* s) * h Hence, L = (6* 4cm) * 10cm == L = 240 square centimeters. 2) Lateral area of a Pyramid: A pyramid is a 3-dimensional figure whose base is a polygon and has triangular faces meeting at the top vertex (also known as the apex). Lateral area of a pyramid is the sum of the areas of the lateral faces of the pyramid structure, without including the area of the base. Just like a prism, there are different types of pyramids based on the shape of its base. If the base of the pyramid is a triangle, then it is known as a Triangular Pyramid. If the base of the pyramid is a rectangle, then it is known as the Rectangular Pyramid. If the base polygon is a regular polygon, then we get a regular pyramid. If the base polygon is an irregular polygon, then the pyramid formed is an irregular pyramid. Lateral Area of a Regular Pyramid = 1/2 * (Perimeter of the base) * (Slant height of the pyramid) (Note: Slant height is the perpendicular altitude drawn from the apex (vertex) to the base of the lateral triangle as shown in the above figure). Lateral Area of an Irregular Pyramid = Sum of the areas of each lateral triangular faces a) Lateral Area of a Square Pyramid: A square pyramid is a pyramid which has a square base. If the side length of the square base is a, then the perimeter of the square base = 4 * a Let the slant height which is the perpendicular distance drawn from the apex to the base of the lateral triangle be = s Lateral Area of a Square Pyramid = 1/2 * (Perimeter of the Square base) * (Slant height of the pyramid) = 1/2 * 4a * s = 2 * a * s Therefore, Lateral Area of the Square Pyramid = 2 * a * s Example: Find the lateral area of a square pyramid whose square base has a side length of 5m and its slant height is 9m. Given side length of the square base of the pyramid, a = 5m Slant height of the pyramid, s = 9m Lateral area of the Square Pyramid = 2* a* s = 2* 5m * 9m = 90m2 b) Lateral Area of a Triangular Pyramid: A pyramid consisting of a triangular base is known as the Triangular Pyramid. In general cases, the base triangle is an equilateral triangle and therefore it is an equilateral triangular pyramid, also known as the regular triangular pyramid. But in case the base triangle does not have equal sides, then the pyramid is known as the irregular pyramid. If the side lengths of the base triangle are a, b, and c, then the perimeter of the triangle = (a+ b+ c) Let the slant height of the pyramid = s Then, Lateral Area of the Triangular pyramid = 1/2 * (a+ b+ c) * s Example: Calculate the lateral area of an equilateral triangular pyramid of base side of 6m and slant height of 10m. Given the side of the base equilateral triangle, a = 6m (Equilateral triangles have equal sides) Hence, a = b = c = 6m Slant height of the pyramid, s = 10m Lateral area of the triangular pyramid = 1/2 * (a+ b+ c) * s == L = 1/2 * (6+ 6+ 6) * 10 = 90m2 c) Lateral area of a Pentagonal Pyramid: A pyramid consisting of a pentagonal base is known as the pentagonal pyramid. A pentagon is a polygon consisting of 5 sides. If the base pentagon has side lengths of a, b, c, d and e, then perimeter of the pentagon = sum of all its sides = (a + b + c + d + e) Let the slant height of the pyramid = s Lateral Area of a Pentagonal Pyramid = 1/2 * (Perimeter of the base pentagon) * (Slant height) So, Lateral area of a Pentagonal Pyramid = 1/2 * (a+ b+ c+ d+ e) * s Example: Given the side lengths of a regular pentagonal pyramid as 5cm and the slant height of the pyramid as 12cm. What is the lateral area of this regular pentagonal pyramid? A regular pentagon has 5 equal sides. Given the side lengths of the base pentagon as a = b = c = d = e = 5cm Slant height of the pentagonal pyramid, s = 12cm Lateral area of a Pentagonal Pyramid = 1/2 * (5+ 5+ 5+ 5+ 5) * 12 = 150cm2 2) Lateral Area of a Cylinder: Cylinders are commonly observed in our daily life. A cylinder is a 3-dimensional solid closed figure and it consists of 2 congruent circular bases that are connected by a curved surface. A cylinder has 2 congruent circular bases and they are parallel to each other. The perpendicular length between the 2 circular bases is known as the height of the cylinder or the altitude. For a given cylinder, let the radius of the circular base = r Let the height (or altitude) which is the perpendicular distance between the 2 circular bases = h Then the lateral area of the cylinder is given by the equation below: Lateral Area of a Cylinder = (Circumference of the circular base) * (Height of the cylinder) Therefore, Lateral Area of a Cylinder = 2 * ???? * r * h Example: Calculate the lateral area of a cylinder whose radius of the circular base is 6m and the height of the cylinder is 8m. Given the radius of the circular base, r = 6m Height of the cylinder, h = 8m Lateral area of the cylinder = 2 * ???? * r * h == L = 2 * 3.14 * 6m * 8m = 301.44 m2 3) Lateral Area of a Cone: A cone is a 3-dimensional figure which has a circular base connected with the single vertex on top (also known as the apex) by a curved surface. The height of the cone is the perpendicular distance from the vertex to the center of the circular base. The slant height is the distance along the surface of the cone from the vertex to the circle, as shown in the figure on the right. For a given cone, let the radius of the circular base = r Let the height of the cone = h and the slant height of the cone = s From the figure we can see that slant height, s = (h2 + r2) (Using the Pythagorean Theorem) Then the lateral area of the cone can be calculated as follows: Lateral area of the cone = ???? * r * s Therefore, Lateral Area of the Cone = ???? * r * (h2 + r2) Example: Calculate the slant height and the lateral area of the cone if the radius of the cone is 6cm and the height of the cone is 8cm. Given radius of the cone, r = 6cm Height of the cone, h = 8cm Slant height, s = (h2 + r2) = (62 + 82) = 10cm Lateral Area of the Cone = ???? * r * (h2 + r2) = 3.14 * 6 * (62 + 82) = 188.4 cm2 4) Lateral Area of a Sphere and Hemisphere: A sphere is a 3-dimensional geometric figure perfectly symmetrical in shape. It is a closed figure formed by points which are equidistant from the center. A sphere has no edges (sides) or vertices (corners). If the radius of a sphere is r, then we can calculate the lateral area as shown below: Lateral Area of a Sphere = 4* ????* r2 When a sphere is cut into equal halves, then we get a Hemisphere. Therefore, the lateral area of a hemisphere is half of the lateral area of the sphere. Lateral Area of a Hemisphere = 2* ????* r2 Example: If the radius of a sphere is 5cm, then what is the lateral area of the sphere and the hemisphere? Given the radius of the sphere, r = 5cm Lateral Area of the Sphere = 4* ????* r2 == L = 4* 3.14* (5cm)2 = 314 cm2 Lateral Area of the Hemisphere = 2* ????* r2 == L = 2* 3.14* (5cm)2 = 157 cm2