Area of Triangle

                                                                                                     
The closed figure that is formed by least the number of line segments that is three line segments is known as a triangle. There are different types of triangles that are classifies on the basis of their sides and angles.

The triangles are that classified on the basis of lengths of the sides are

(i) Scalene
(ii) Isosceles
(iii) Equilateral

The triangles are that classified on the basis of the measures of their angles are

(i) Acute angled
(ii) Right angled
(iii) Obtuse angled

Online Geometry Tutoring helps you to solve all the homework problems

Scalene Right Triangle

A scalene right triangle is a three sided figure in which all the three sides are different from each other and one of the angle measures 90 degrees.

Finding Area of a Triangle

Area of any three sided figure (triangle) is the region that is enclosed by the three sides of the figure. This can be found using different formula.

Formula : 1

Area = ½ * base * height
Where base is the side on which the altitude is drawn, height is the length of the altitude that is drawn on the corresponding base.

Example : 1

Find the area of the figure given below.

Solution :

In the given figure, we see that the altitude AD is drawn on to the side BC of the triangle. Therefore, Base = BC = 8 cm and height = AD = 3 cm.

We know, area = ½ * base * height
                            = ½ * 8 * 3
                            = ½ * 24
                            = 12 square cm


Example : 2

Find the area of a three sided figure whose sides lengths are 4 cm, 5 cm and 3 cm.

Solution :

Given, the three sides are
1st side = 4 cm
2nd side = 3 cm
3rd side = 5 cm

These three sides form a Pythagorean triplet. In which 4 cm and 3 cm are the lengths of the legs (that is the sides containing the right angle)

Therefore, Base = 4 cm and height = 3 cm.
We know, area = ½ * base * height
                        = ½ * 4 * 3
                        = ½ * 12
                        = 6 square cm

Formula : 2

If a, b and c are the lengths of all the sides of a triangle then its area is found using the formula
Area = square of root of [s(s – a)(s – b)(s – c)] square units

Where S is known as the semi perimeter and is found by sum of the side lengths divided by 2

Example : 3

Find the area of the triangle whose sides lengths are 6 cm, 7 cm and 9 cm

Solution :

Let a = 6 cm, b = 7 cm and c = 9 cm

Semi perimeter = (a + b + c)/2 = (6 + 7 + 9)/2 = 22/2 = 11 cm
s – a = 11 – 6 = 5
s – b = 11 – 7 = 4
s – c = 11 – 9 = 2

Area = √[s(s – a)(s – b)(s – c)] square units
Area = √[11(5)(4)(2)] square cm
Area = √[440] square cm
Area = 20.78 square cm

Example : 4

Find the area of the triangle whose sides lengths are 10 cm, 12 cm and 14 cm

Solution :

Let a = 10 cm, b = 12 cm and c = 14 cm

Semi perimeter = (a + b + c)/2 = (10 + 12 + 14)/2 = 36/2 = 18 cm
s – a = 18 – 10 = 8
s – b = 18 – 12 = 6
s – c = 18 – 14 = 4

Area = √[s(s – a)(s – b)(s – c)] square units
Area = √[18(8)(6)(4)] square cm
Area = √[3456] square cm
Area = 58.79 square cm

Formula : 3

If all the sides of the three sided figure are congruent to each other. Then such a figure is known as equilateral triangle.
Area = (√3/4)(a²) square units.

10 Effective Fundamentals For Teaching Math

Teaching math to the students can be a forbidding task for many of the math tutor and parents because math is a different subject compared to other subjects. The teacher should know the teaching fundamentals of math before they go to math class. What if the teacher knows all the fact of teaching math but cannot communicate to the students in a way so that students understand it? For teaching math teacher needs a student’s friendly communication. 

Below you can find 10 effective fundamental for teaching math,

1) Teaching should make some sense. Explain math concepts to the children so that it makes some sense. Many students hate math engage them in such a way so that they learn to enjoy math.

2) Encourage students to learn math. Involve such math activities in your teaching which encourage students to do math.

3) Math is a subject which is different from other subjects. Some students need more time to understand the math. Teach math concepts not just to memorize, explain concepts in such a way so that it helps children to learn exactly how the math work and they can apply their knowledge in other problem too.

4) Students learn differently. Use different methods of teaching. For examples some students are weak in statistics, provide Online Stats Help with live examples. Like vies concentrate on each student’s weak parts of math. Use worksheet, flash cards other techniques of teaching.

5) People learn from failure. Allow students to do mistakes, this will help students in some points.

6) Let students teach you. This is one of the most effective method or teaching math.

7) Before moving to the next topic make sure student completely understands the concept.

8) Games are the best way to enhance math learning. Enhance Students math learning by objects round them.

9) Math is a subject with almost everyone hates. The best way to teach math is rewarding students for their success. This will give them confidence and encourage them to do better.

10) Learning feedback matters. Telling students, their weakness and strengths also help them in the same way as failure.

Follow these 10 effective fundamental ways to teach math and allow students to make the math simple. To know more about it click here.              

10 Practical Tips To Improve Math Skills

Math is an important skill in everyone’s life. Mastering math skills is very essential for future opportunities. Math made easy to achieve any success. Parents and teachers need to motivate the students to improve their math skills. If your child is struggling with math skills, here are a few tips that will help you to improve their math skill,

1) Make sure that your child is able to understand the mathematical concepts. If not, try to explain in different ways. Otherwise, math will become meaningless for them.

2) Start with algebra basic concepts. First, let them master the basic facts of math. You can use flash card, manipulate objects, Online Algebra Tutor for your children to learn the basic concepts.

3) Let your children to enjoy the math. Games are the best ways to enjoy the math. For example, chess will teach them planning strategies. Games help students to improve their math skills in a better way.

4) Provide immediate help to your children whenever they need it. Math is a subject in which everything is built upon what has been learned before. Immediate help will allow students to work further. If you are not able to help your children, then you can provide them a free online tutor. They are available 24/7 to help your children.

5) Help your children to understand math symbols and vocabulary. Without a proper understanding of math symbols and vocabulary students are not going to get a feeling to learn math.

6) Encourage students to do more than assignments problems. Practice needs to improve math skills.

7) Show your children different method of solving problems. This will allow your children to find out which technique suite them most.

8) Play number guessing games with your children. This helps you to improve their number sense.

9) Connect math concepts with real world examples so that it will be easy to remember for children.

10) Provide puzzles to solve your children. The puzzles are the best way to develop math skills. Parents can develop puzzles for reviewing their preparation for exams.  

By implementing these 10 tips your child will be able to perform better in math.

How Can I Develop Math Confidence?

Remember that some amount of anxiety is helpful to keep us motivated and energized about something. However, if your anxiety is so great that it is interfering with your ability to do well in class, there are some steps you can take:

• Do math every day

Just like with a foreign language, if you don't use math frequently, you'll have a harder time becoming fluent. Do some math every day (Yes, including weekends), even if it's only 15-30 minutes. Try to avoid stacking all of your math activities on one or two days.

• Scheduling

Build positive time management skills by making and sticking to a reasonable schedule. Your schedule should include time for studying, as well as social and personal activities. There are many ways to make a schedule; find what works best for you.

• Prepare adequately

Make sure you're going to every class and regularly reading your math textbook. Use you TAs and academic resources on campus. For larger projects, start early rather than waiting until the last minute.

• Identify and eliminate negative self-talk

Become aware of your internal dialogue. Start replacing negative self-talk with more affirming and rational self-talk. This may feel funny at first, but it will start feeling natural the more you practice.

• Practice good self-care

Get enough sleep. Eat well-balanced, regular meals. Participate in a regular exercise program. Learn effective ways to relax and manage stress and anxiety. Poor self-care leads to poor performance in all areas, including math.

• Seek help

Find a study buddy or study group. If you feel you need additional assistance, seek out a tutor or counselor. The Counseling Center offers a group to help students gain math confidence. Don't let fear of asking for help keep you from reaching your goals.

Blog Courtesy - http://www.counseling.ufl.edu/cwc/developing-math-confidence.aspx

Math Vocabulary Categories For High School Students

For any high school student the subject choosing depends upon which are the topics they are strong in or fancy about to carry on scoring. The first thing that helps these students is choosing by difficulty level. Then the next best thing they always look for is the terminologies these topics carry. Students have very strange way of behaving and selecting topics and they always have some or other reason for either choosing or rejecting a topic.

Some students fancy difficult terminologies for each sub-topic as something very colorful while another lot might detest the very same terminologies and select some other subject if given a chance. These terminologies in mensuration, trigonometry, geometry and arithmetic progression are basically one way of representing a certain operation and once a student get used to these terms they could always go ahead use these for discussion.

Students make sure that they do not fall behind in case it involves remembering these terms in algebra vocabulary or trigonometry vocabulary. As after sometime the same difficult terms becomes a style statement for some. As they flaunt these in front of others to show that they know better and or have covered more than the rest.

Sometime Math Assignment Help might help them with these terminologies and they might make use of these terms to learn their application. Once they are quite used to these terms and application they might even think of doing these on their own.

For any high school students the knowledge and proper one about the topics is essential as most of the assignment that they get will not be tailored made of their choice. Knowing only the terms is not enough. Their application and how they are utilized is also essential.

For each topics and their sub topics there are innumerable terms and for each specific vocabulary there is specific function or operation. None of the terms might have anything crossing over meaning and so the distinct operational function.

Solving math word problems is always a challenge and as always has specific terms for each operation and carries key formulas. For these a student has to know not only the key formulas but also make enough effort to know the vocabulary and use appropriate steps to get to the answer.

There are terminologies like matrix and matrices which has same meaning but different way of pronounced and yet the student being aware of such malady knows what is to expect and what exactly these two terms lead to.

Yet again there are terms like exponent and indices which has same operation and so makes perfect pair of terms which has same working operation but different origin. There are tutors who help with these topics and especially when one is dealing with math assignment help. These kind of help is always welcome and essential as well because without these help one might get completely lost in the myriad world of math vocabulary and make unforced errors.

Tips On Solving Algebraic Equations

It’s always better to make a mistake at the beginning than make a mistake after the concept has been imparted. Imparting a new concept is always difficult and it’s even more difficult to know whether the student has learned it proper.

Getting the student to understand the meaning of variables and why a variable would be so important to set up an algebraic equation and then solve it as well.

The first thing one has to understand is the instruction and the variables that are taken for the unknowns. The next step would be to isolate the variables in question by using addition, subtraction, division or even multiplication. For each of these operations the main thrust still remains to get to the unknown by the shortest possible route and hence the perfect equation.

Once the equation is ready it’s always easy to get the rest done quickly. One has to remember the identity rules proper as these are getting used every now and then for solving.

The first step in solving is writing the correct equation. In case the equation doesn’t match the expected unknown then the equation will end up in error.

In some instances the Online Math Tutoring helps a lot in sorting out these kinds of doubts. The tutor could help the student on a daily basis and in turn the student always can go ahead and clear his doubts whenever and whatever topic he needs help in and not only just algebra.

Pre-algebra math help is basically about the key skill area of know about the variables and how or when these are applied. Mostly these topics are sought after for recalling the concepts and work further to get the basics clear. Teachers need to be extra cautious for such topics as the student might be looking for just reviving what knows already.

The whole idea of solving algebraic equations is based on the denotations that require the inputs from the known value and setting up of a relation between the known and unknown factors. The known values are always denoted with the values they carry and the unknown ones are usually represented with variables which could easily be identified.

Once the factors are known these are collated into a working relation where we could isolate the unknown on one side the rest on the other. Then the operation involving addition, subtraction, division and multiplication are taken into account and applied wherever necessary to get the unknown value.

The changes that we make on either side have to same on both sides. Whatever operation we make or bring changes in one side we need to balance out on both sides and that is the golden rule of algebra.

In the last but one step before we get to the answer we have to make sure to eliminate the coefficient of the unknown variable by either division or multiplication which leads us to the ultimate answer.

In case there are two unknowns then we need to use two variables and make use of a working relation to solve for one variable first and then go for the next one. Until we get one of these we may not get the other one as well. In algebra the working relation between the variables is very important and that helps in reaching the final answer.