Tetrahedron properties

For a regular tetrahedron of edge length a:

 Face area

Surface area^[2]

Height of pyramid^[3]

Edge to opposite edge distance

Volume^[2]

Face-vertex-edge angle

Face-edge-face angle^[2]
Edge central angle,^[4][5] known as thetetrahedral angle
Solid angle at a vertex subtended by a face
Radius of circumsphere^[2]

Radius of insphere that is tangent to faces^[2]

Radius of midsphere that is tangent to edges^[2]

Radius of exspheres

Distance to exsphere center from the opposite vertex

Find the volume of an irregular tetrahedron form its edges:

Suppose you are given the 6 sides of an irregular tetrahedron and you need to find the volume consumed by it.

Let the given sides to be u, v, w, W, V, U. Here, (u, U), (v, V), (w, W) are considered to be opposite edge pairs ( opposite edges means the edges which do not share common vertices ). Now the volume can be found from the following formula:

Let:
u′ = v² + w² - U²
v′ = w² + u² - V²
w′ = u² + v² - W²
Now:
volume = ¹⁄₁₂ × √(4u²v²w² - u²u′² - v²v′² - w²w′² + u′v′w′)

This formula is derived from the determinant which can be found here for more reading. As the formula is symmetric, the ordering of the pairs won't make any change to the formula.

Multiplication Tips and Tricks

Some Tips and Tricks

It is best to put the whole table into your memory using Math Trainer - Multiplication, but here are some tricks that may help you remember your times tables.

Everyone thinks differently, so just ignore any tricks that don't make sense to you.

The Best Trick

Every multiplication has a twin, which may be easier to remember. For example if you forget 8×5, you might remember 5×8. This way, you only have to remember half the table.

Tricks by Number

to multiply by	Trick
2	add the number to itself (example 2×9 = 9+9)
5	the last digit goes 5, 0, 5, 0, ...
	is always half of 10× (Example: 5x6 = half of 10x6 = half of 60 = 30)
	is half the number times 10 (Example: 5x6 = 10x3 = 30)
6	when you multiply 6 by an even number, they both end in the same digit. Example: 6×2=12, 6×4=24, 6×6=36, etc
9	the last digit goes 9, 8, 7, 6, ... your hands can help! Example: to multiply 9 by 8, hold your 8th finger down, and count "7" and "2", the answer is 72
	is 10× the number minus the number. Example: 9×6 = 10×6−6 = 60−6 = 54
	when you add the answer's digits together, you get 9. Example: 9×5=45 and 4+5=9. (But not with 9×11=99)
10	put a zero after it
11	up to 9x11: just repeat the digit (Example: 4x11 = 44)
	for 10x11 to 18x11: write the sum of the digits between the digits Example: 15x11 = 1(1+5)5 = 165 Note: this works for any two-digit number, but when the sum of the digits is more than 9, we need to"carry the one". Example: 75x11 = 7(7+5)5 = 7(12)5 = 825.
12	is 10× plus 2×

Remembering Squares Can Help

This may not work for you, but it worked for me. I like remembering the squares (where you multiply a number by itself):

1×1=1	2×2=4	3×3=9	4×4=16	5×5=25	6×6=36
7×7=49	8×8=64	9×9=81	10×10=100	11×11=121	12×12=144

And this gives us one more trick. When the numbers we are multiplying are separated by 2 (example 7 and 5), then multiply the number in the middle by itself and subtract one. See this:

5×5 = 25 is just one bigger than 6×4 = 24

6×6 = 36 is just one bigger than 7×5 = 35

7×7 = 49 is just one bigger than 8×6 = 48

8×8 = 64 is just one bigger than 9×7 = 63

etc ...

how to handel a maths problem?????

When beginning to work a Math problem, do not "map out a path from problem-to-answer" in your head before writing anything down. I see this almost every day. It is very common when someone looks at a Math problem that they try to "figure it out" in their head before writing anything down. Take Algebra for example. When a beginning student looks at an equation, he or she will be tempted to solve the equation in their head and not write anything down. Students are tempted to do this most often with Word Problems. Since a word problem is written in sentence form, it is common to think that you can "think your way to the answer". I will tell you that I never, ever, solve any sort of math problem without writing it down. Ever.

What you need to do is begin by first writing down the problem. Then you begin to solve it one step at a time. Write down even the simple things. What you need to ensure is that every single step that you write down is perfectly legal. In other words, if you are solving an equation for example and you subtract "10" from both sides....write that down. Then in the NEXT step actually do that subtraction. Then if you need to divide both sides by "2" write THAT down...then in the NEXT step actually do the division. This gives you a paper trail to check your work and also it allows you to break the problem down in to bite sized chunks. If you can be sure that every single little step is legal, then you will be in good shape. If you try to do too many things at one time, which is common, you will probably try to do something illegal and get into trouble.

All the basic math formulas app for android

 https://play.google.com/store/apps/details?id=com.nsc.mathformulas.lite&hl=en

to improve your maths Skill

If you don't understand something, focus on mastering that topic before moving on to the next topic. It sounds simple, but it is absolutely essential. Lets say a student is learning Algebra, for example. Further, lets say he or she is having a hard time understanding how to add and subtract negative and positive numbers. All of us struggle with this in the beginning as it is a sticky point for most students. Some students in this situation, out of frustration that they "can't" learn this topic, will move on to the next lesson in the hope that they will be able to understand that one.

This is a recipe for disaster.

Math is very much like learning to read. If you don't know your letter sounds then you have no hope of being able to sound out words of course there is no way possible that you could read a book. All math courses are taught in a specific sequence because the every topic builds on the previous topic. If you are having a problem with a topic, continue working with that one until you understand it and can work problems successfully. Watch the DVD section over again, attend tutoring, read the book and examples a second time, or even get a totally different book to have it explained a different way...but whatever you do not turn the page and tackle the next topic. If you do, you will get even more frustrated and you in all likelihood will begin to give up hope.