Formula of the znakhozhennya area of the tricot tricycle know. The yak knows and the area of the tricot (formulas)
To help your child with lessons, the fathers are guilty of the nobility themselves without words. How do you know the area of a tricot tricycle, what is the accrual turnover from the deduction, how is the speeding up of the deed?
Be-yakim іf chih food at your son and daughters may be aware of problems, and the stench itself is up to you to turn for the roses. Why not fall into denunciations from a bugnyuk and to gain his authority in the eyes of a child, to revive in the memory of deyaki elements of school programs.
Vіzmemo for a butt of food about a tricytric equestrian. Geometry in schools is important to give, and for schools it is best to forget.
If your children are at the 8th grade, you will have a chance to guess the formulas of geometrical figures. The tricycle tricycle is one of the simplest figures in the plan of the known parameters.
Yaksho everyone, you know, they’ve read about trikutniki, they’ve forgotten, let's zgaduvati. Rivnostegnovim to be called such a trikutnik, which has 2 sides and may have the same amount of dinner. The ribs between the ribs are called the side sides of the femoral tricycle. The third party is yogo p_dstava.
It is such an option, with each level being on all 3 sides. Vin man will name a one-sided trikutnik. All the formulas are extended to new ones, which can become stagnant to the level of the femur, and in times of use, whether from this side can be called the basis.
For the knowledge of the area, we need to distribute the basis of the navpil. Straight, lowered to the otrimano point from the top, scho from the bottom side, overflowing the base with a straight cut.
The same is the power of such tricytes: mediana, to be straight from the top to the middle of the opposite side, in the tricot tricycle є with a bisectrix (straight, to extend the cut navpіl) and thigh length (perpendicular to the side to the opposite side)
To know the area of a tricot tricycle, you need to multiply its height on the base, and then add it to the base.
For znakhozhennya area of a tricot, the formula is simple: S = ah / 2 de a - Dovzhin basis, h - visota.
In fact, the price can be explained as follows. Look at the paper similar to the figure, know the middle of the base, draw the height to the center point and carefully distribute it along the height. Take two rectangular tricycles.
If you attach them one to one with hypotenuses (with both sides), then a rectangle will appear, one side of which is more than our figuri, and іnsha - half asleep. To confirm the formula.
At the same time, the demonstration is even more important. As soon as your child is not mindlessly memorizing the formulas, it’s the intelligence and geometries that cannot be seen as a folding object.
Let's learn from the class that the class is not jagged, but thoughtful, smut, schoolboy, wisdom.
Yak know the area of the figuri, how is one kut straight?
It can be seen that the cut between the sides of the given tricot figure becomes 90 °. Toddler tricycle is nazyvatimetsya rectangular, one side - legs, and the base - hypotenuse.
The area of such a figurine can be counted in the lower end (the middle of the hypotenuse is known, it is carried out to its height, multiplied by the hypotenuse, then it is navpil). If not, the problem can be resolved, but the problem is simpler.
For some reason. Straight-cut tricycle tricycle є in half a square, which is diagonal. If the area of the square is located at the other steps of the other side, then the area that we need will be a little less.
S = a 2/2, de a - Dovzhin's leg.
The area of the rectangular tricycle is on the side half of the square on the side. The problem appeared not so serious, like a bully for a first glance.
The show of geometric buildings is not a vimage of over-human beings, and at all, it is not just children, but you, if you know anything about practical nutrition.
Geometry is an exact science. If you look into the foundation, then it will be difficult because of it, but the logic of proof can still grab your child. You just need help. Yaky bi-kind teacher of youmu did not get away, I won’t get help from my father.
And in the development of geometries, the method, about which they spoke, is even more clear-cut.
At the same time, it is impossible to forget about the exactness of the formula, but it is possible to develop a science in a way that is folded, but not for sure.
Have tsіy statti mova pіde about those who know area of the femoral tricycle and formulas for vir_shennya.
Tricycle tricycle tricycle tricycle, at which two parallel lines are the sides of the tricycle
... Win images of the little one.
To respect Varto, how much lithi with the meaning of the sides and kuti, vikoristoyutsya at the formulas, for your vitality.
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The area of the femoral tricycle formula.
The first formula is to talk about those who are located, as far as we can see only one side is the basis of the trikutnik... We took the qiu formula after the supplementary formulas. If the main thing is that Heron's formula is that the sides of the figurine are simpler.
The other formulas are about those that are located through bichni sides and kut, where to be found among them... For sin kuta is located between the family sides, multiplications by half of the square of one of the family sides. If it is carried out to the side of the side, dovzhina, a * sin ?. So, as I know it’s on both sides, we’ll see it. Apparently, the area of the tricycle tricycle will be half of the bend. I'm more accurate. This is the value to rob the area of the tricycle. Rozdіlyayuchi with a height of a rectangle, we will recognize two small rectangular trikutniks. Diagonal will be the side of the tricycle, at its own heart, there is a figurine on two separate parts. Wow, what a shukan we value is half the size of one side, so it multiplies by the height.
The third formula has an area for help one parallel side, the base of that kuta, which is located on the top... So you can say this: if you want one cut in a tricot, you can know and two others. The qia formula is similar to the other formula, it is possible to vikoristovuvati and remember to be with them. Ale z tsієї formulas viide p'yata, yaku I will describe the trochies below.
The fourth formula will show you how to know the area I know the value of the base ta kuta for new... All cutouts are based on the same, and the square of the sides is the base of distributions for 4 tg cut, which appeared from each side. If you respectfully look, it is possible to look at the side of the base b / 2, with multiple tg (? / 2) yes to the height. Yaka its own distinction is the role of median and bisectrix, even tg (? / 2) = (b / 2) / h, from which h = b / (2tg (? / 2)), and it is built up to the simplified formula No. 5.
Otzhe, p'ata formula won’t talk about those who can know the area. for help as I take the cob at the top of the tricycle and end at the first tricycle. And given in the third and fourth formulas. The value of the height is multiplied by the value of the base.
Shosta is the enclosed formula. Vona appears before the hour of the tricutnik square via Pyfagor's theorem... We know the height, which is known from the coli formulas. Vaughn itself is brought with the leg out of the rectangular tricycle, scho viyshov from the side, half of the base plus the height. The hypothenuse will be on the side, from the square of the hypotenuse (a) we will take another leg from the square. So yak vin dorivnyu pidlozi - stem (b / 2) means square = b2 / 4. Viimayuchi is the root of the rejected, we know the visota.
Instructions
Video on the topic
Beast to respect
Dzherela:
For the ear of home about the meaning. The leg is called the side of the rectangular tricycle, the yak is lying down to the straight kut (tobto the warehouse from the іnshy side of the kut 90 degrees). Dovzhini cathetіv understandable to start a and b. The size of the gostrich kut_v of a rectangular tricycle, which can be extended to the legs, is called A and B as a matter of fact. Hypotenuse is the name of the bik of a rectangular tricycle, which is opposite to a straight kuta (so that it is located right next to a straight kuta, with the other sides of a tricut I will make a gostri kuti). Dovzhinu hypotenuzi is meaningful through s. Shukanu square is meaningful through S.
Instructions
Stay in the formula S = (a ^ 2) / (2 * tg (A)) at that vypadku, if you have tasks deprived of one of the legs (a), or also vіdomy kut (A), to support the th leg. The sign "^ 2" denotes a square.
Victory the formula S = (a ^ 2) * tg (B) / 2 d y vypadku, if you do not have tasks with one of the legs (a), but also the vidomy cut (B), which is attached to the leg.
Video on the topic
Dzherela:
- "Book of Mathematics for Entrants to Higher Educational Institutions", ed. G.M. Yakovlev, 1982.
Rivnostegnovim vvazhaєtsya such a trikutnik, at which two sides of the ryvnі. The area of a tricycle can be developed using several methods.
Instructions
Video on the topic
Beast to respect
Find the signs of a femoral tricycle:
1) At a femoral tricycle є 2 rivnі kuti;
2) The visota of the tricycle is getting rid of the median;
3) The visota of the tricytta bears on the yogo bisectrix;
4) The bisectrix of the tricycle is getting used to this median;
5) The femoral tricycle has 2 median rivnias;
6) The femoral tricycle has 2 lengths;
7) The femoral tricycle has 2 bisectors.
Dzherela:
- tricycle area
One of the figures, which can be seen in the lessons of mathematics and geometry, is a trikutnik. Trikutnik - bagatokutnik, yakogo has є 3 peaks (kuta) and 3 sides; a part of the area, surrounded by three dots, in pairs with three dots. Isnu bezlіch zavdan, tied from the knowledge of the growth of the figures of the figuri. One of them - area... Reserved from the previous tributes, the number of formulas for the area trikutnik.
Instructions
As soon as you see it, the dinner parties were held at its height. trikutnik, Vicorize the formula S =? h * a.
As soon as you see one side of the tricycle of the same height, it is lowered to the side, multiply one side by one side, and distribute the result on two sides.
As long as you are in front of you a straight-cut tricycle, follow the lines of up to the length of your legs, so that the sides, which lie down to the straight cut. Multiply by the number of legs, and the result is reduced by two.
As soon as you can tell about the size of the cut between two tricycles, and you see the tricycles, then I know the area of the tricot by the formula:
St = ½ * A * B * sinα, de St - the area of the tricycle; A and B - dozhini side of the trikutnik; α - kuta, roasted between the sides.
S = 1/2 (AB + BC + AC) = p r.
Calculate the perimeter:
p = (5 + 7 + 10) = 11.
Insure the required value:
S = √ (11 (11-5) (11-7) (11-10)) ≈ 16.2.
Three points that unambiguously represent the tricutnik in the Cartesian coordinate system - the whole vertex. Knowing the position of the skin from the coordinate axes, it is possible to calculate the parameters of the flat figure, including the perimeter. area... The price can be created in a number of ways.
Instructions
Vikoristovyte Heron's formula for area size trikutnik... Have nіy zadіyanі razmіri three sides fіguri, to that count, fix it. Dovzhina of the skin side is guilty of making the root iz the sum of the squares of the dovzhin projections on the coordinate axes. We can denote the coordinates A (X₁, Y₁, Z₁), B (X₂, Y₂, Z₂) and C (X₃, Y₃, Z₃), and in the genie їх sides can be violated as follows: AB = √ ((X₁-X₂) ² + (Y₁ -Y₂) ² + (Z₁-Z₂) ²), BC = √ ((X₂-X₃) ² + (Y₂-Y₃) ² + (Z₂-Z₃) ²), AC = √ ((X₁-X₃) ² + (Y₁-Y₃) ² + (Z₁-Z₃) ²).
To simplify the rosters, enter a supplementary change - for example, a perimeter (P). Z, so half the sumi dovzhin of the sides: P = ½ * (AB + BC + AC) = ½ * (√ ((X₁-X₂) ² + (Y₁-Y₂) ² + (Z₁-Z₂) ²) + √ ((X₂-X₃) ² + (Y₂-Y₃) ² + (Z₂-Z₃) ²) + √ ((X₁-X₃) ² + (Y₁-Y₃) ² + (Z₁-Z₃) ²).
Crack area(S) according to Heron's formula - find the root from the perimeter on the basis of the difference between them and the skin from the sides. The zagal її can be written as follows: S = √ (P * (P-AB) * (P-BC) * (P-AC)) = √ (P * (P-√ ((X₁-X₂) ²) + (Y₁ -Y₂) ² + (Z₁-Z₂) ²)) * (P-√ ((X₂-X₃) ² + (Y₂-Y₃) ² + (Z₂-Z₃) ²)) * (P-√ ((X₁) -X₃) ² + (Y₁-Y₃) ² + (Z₁-Z₃) ²)).
For practical applications, you can manually use special calculators. Tse scripts, distributed on the servers of some sites, such as to create all the necessary space on the basis of coordinates, as entered in the form. One such service is that it’s not enough to explain that rim for skin croc. To that, if you want to be deprived of the final result, and not assessed by the zealous viglyad, go, for example, to the side of http://planetcalc.ru/218/.
In the form field, enter the skin coordinate of the skin from the vertices trikutnik- the stink here yak Ax, Ay, Az, etc. Yakshcho trikutnik tasks with two-dimensional coordinates, at the field - Az, Bz and Cz - write zero. At the "Accuracy of calculation" field, set the required number of signs written by the Komi, clicking with a bear
Mathematics is a divisive science. However, such a thought will only come if it’s not enough. It’s necessary to make sure that you do it, you need it, you need it, you need it, you need it, you need it, you need it, you can use it with theorems.
Go to the rosuminnya geometriya lie through the task of solving problems. With an adjustable butt, you can get a job, for those you need to know the area of a tricot tricycle.
So also a tricycle fitter and in what way do you see them?
Schob does not lyakatya terms "visota", "area", "basis", "ravnostehnovogo tricycle" and others, it is necessary to distribute from theoretical foundations.
A compilation about the tricycle. The whole figure is flat, yak is set at three points - peaks, at its own circle, z'єdnanih іdrizki. If two of them appear equal to one to one, then the trikutnik grows old. Tsi parties rejected the name of the biches, and the rasht became the basis.
The іsnu okremiy vypadok іvno-femoral tricycle - equilateral, if the third party is dorіvnyu two bichim.
Power figuri
Smells appear as vіrіshennі pomichnikov at the virіshennі zavdan, as vimagayut to know the area of іvno-femoral tricycle. That nobility that memory about them is necessary.
- Perche: kuti of a tricot tricot, one side of which is the basis, make one rivni one to one.
- We are important є і power about additional encouragement. Conducted to the unpaired side of the height, the median and the bisectrix are set.
- Tsі and іdrіzki, carried out from kutіv on the basis of a tricycle, in pairs. Tse also often lays down poshuk rіshennya.
- Two rіvnі kuti in new may be less than 90º.
- The first stop: the inscriptions and descriptions of the stake will be so that the center lies on the top to the base of the tricycle, and that means the media and bisectors.
What is the problem of developing a trikutnik fitter?
Whenever you receive a feed supply about those who know the area of a tricot tricycle, then there is a need for intelligence to be brought to the attention of the whole group. And in tsyomu help singing signs.
- Rivni two kuti or two sides of a trikutnik.
- Bisector є other media.
- The visota of a trikutnik appears as a median chi bisectrix.
- Rivni dvi visoti, median chi bisectrix figuri.
The values \ u200b \ u200btaken in the analyzed formulas
In order to make it easier for him to know the area of the femoral tricycle behind the formulas, the replacement of the elements on the lithi has been introduced.
Uwaga! It is important not to cheat "a" z "A" ta "in" z "B". The price of the size.
Formulas that you can speed up at the new employees
From the house to the side, and it is necessary to know the area of the femoral tricycle.
In general, it is necessary to square the offense value. The number that was seen from the side of the wrinkle, multiply by 4 and see from each other. Z otrimano іznitsі vityagti square root. Dovzhinu base razdіliti by 4. Multiply two numbers. If you write it down by letters, then you see the following formula:
Nekhai won will be recorded as # 1.
To know the area of the femoral tricycle beyond the significant sides. The formula, as someone can be simple, nizh persha.
The first step is to know half of the basics. Let us know the bag with the difference in number from the side. The two remaining values are multiplied and the square root. With the rest of the day, multiply everything by half of the basis. The letter of parity is as follows:
Tse formula number 2.
How to know the area of the tricot tricycle, which is the basis and height to the new one.
One of the shortest formulas. They need to multiply the grievances of the values and distributions by 2. The axis of yak will be written:
The formula number is 3.
At the front of the side of the tricycle, the meaning of the kut, which lies between the base and the side.
Here, schob d_znatisya, because of the large area of the femoral tricycle, the formula is composed of decilkokh multipliers. The first is the value of the sinus kuta. Another door is added to the side on the base. The third is drib ½. Zagalny math notation:
The ordinal number of the formula is 4.
The task is given: the bichna side of the tricycle tricycle is that kut, which lies between the bichy sides.
Yak і in the forefront, the area is located in three multipliers. The first one is the meaning of the sinus kut, given for the mind. The other is the square of the side. The first remaining half of the unit is also expensive. The formula for the result will be written as follows:
Її number - 5.
The formula, as it allows you to know the area of the femoral tricycle, as if it is the basis of that kut, which lies on the ground.
From the list, it is necessary to calculate the tangent of half of the home kut. Otriman multiply the number by 4. Bring to the square on the side of each side, as the space on the opposite side. In such a rank, viide, this is the formula:
The number of the last formula is 6.
Put on the zavdan
Perse zavdannya: vіdomo, scho the basis of the іvno-femoral tricycle is 10 cm long, and the thigh height - 5 cm.
For the first time it is logical to vibrate the formula number 3. Everything seems to be there. Give the date that porahuvati. Wiide, which has a road area of 10 * 5/2. Tobto 25 cm 2.
Other zavdannya: in a tricycle tricycle is given a bichna side that basis, which is equal to 5 and 8 cm. Know this area.
The first method. For formula number 1. When the base is squared, the number 64 should be entered, and the four-fold square of the bithy side is 100. Writing from another first view is 36. It's a miracle to find the root, which is the way to go 6. The base is added to 4; і 6, tobto 12. Tse vіdpovіd: the required area is 12 cm 2.
Another way. For formula number 2. Half of the base is 4. The sum of the lateral side and the known number is 9, the value is 1. The number of entries is 9.
Virishyuchi zvdannya z geometrії and viznachayuchi, as to know the area of the tricycle tricycle, it is possible to deduct neo-rated information. If there are more new options for the Viconano establishment, it's easier for you to know the new situation. To that, the independence of all buildings is regularly maintained until the successful mastery of the material.
Lіternі poznachennya sides and kutіv on the directed little unit will show the meanings, we mean in the formulas. With such a rank, it will help you to match the elements of the tricot tricycle. Take into account the details of the items you see, know on the armchairs the designated and accept the formula.
Formula of the area of the femoral tricycle
Dali directed formulas for the knowledge of the area of the femoral tricycle: through the sides, the bichu side that kut between them, through the bichnu side, the base that cot at the tops, through the bik base that cut when presented, etc. Just know the best way to go to the kid. For those who find the text right-handed, it will be explained why the formula є is correct and that it is possible to be found in the area.
- you can know know yogo bik that basis... Tsei viraz bulo otrimano by way of forgiveness of the larger, universal formulas. Just take Heron's formula as a basis, and then take the two sides of the tricycle with honey as a basis, and then say goodbye to the formula presented in the picture.
The butt of the victorian of such a formula is aimed at the attachment of the problem solving below. - Another formula allows you to know your area through bichnі sides and kut between them- half the square of the lateral sides, multiplied by the sine of the cut between the lateral sides
If you think about lowering the hang on the side of the ryvno-femoral tricycle, it’s great, that її dovnina dorіvnuvatime a * sin β. Oscillations of the bite to the sides of the house to us, the visota is lowered on it now, half of the work and the large area of this tricycle tricycle. є їх diagonals, which range іх equally navpіl, in such a rank, the area of the femoral tricycle and the half of the side to the top). also Formula 5 - The third formula for showing the area across the side, the base is at the top.
Strictly it seems, I know one of the hips of a femoral tricycle, you can know that one, the one given, or the foremost formula, is nourishing gusto (before the speech, one can forget one of them).
The third formula also has one tsikava specialty - tvir a sin α give us a whole lot of weight, lowered onto the base. As a result, the obvious simple and obvious formula 5. - The area of the femoral tricycle you can also know through bik basics that kut at delivery(kuti at the base of rivni) yak the square of the base, on the chotiri tangential half of the kut, adopted by the other sides. Yakshto pride yourself respectfully, it becomes obvious that half of the base (b / 2) is multiplied by tg (β / 2) to give us the height of the tricot. Oscillations of the height in the tricot once bisectrix and median, then tg (β / 2) - the price of half of the base (b / 2) to the height - tg (β / 2) = (b / 2) / h. Stars h = b / (2 tan (β / 2)). In the result, the formula will be brought back to the simple Formula 5, which is quite obvious.
- Zrozumіlo, area of the femoral tricycle You can know by lowering the height from the top to the base, as a result of which you will see two rectangular tricycles. Dali - everything is obvious. Half a twist on a baseі required area. Butt vikorystannya given formulas div. at tasks lower (2nd way of connection)
- The qia formula is to go, if you try to know the area of the femoral tricycle behind the addition of Pyfagor's theorems... For a wide range of variations in front of the front formula, like one hour є with the leg of a rectangular tricycle, fixed by the side, half of the base and the head, through the Pyfagorian theorem. Bichna side є hypotenuse, to that from the square of the bichy side (s) the square of the other side is visible. Oskilki vіn dorіvnyu half of the base (b / 2) then the square is dorіvnyuvatime b 2/4. Forces of the root from tsyogo viraz and give us a hang. It can be seen in Formula 6. You should multiply the number and the standard by two, and then add the root sign for two numbers, we can accept another version of this formula, which is written through the sign "equal".
Before the speech, you can play it, but if Formula 1 has the arches, then you will be reimagined to Formula 6. Anyway, the navpaki, the growth of squares of two numbers, is multiplied, to give us a wiggle, pershu.
Designation, like boules are stuck in the formulas for a little:
a- Dovzhina one from two sides of a trikutnik
b- Dovzhina bases
α - the size of one of two double kutіv at the podstavі
β - the size of the cut between the flat sides of the tricycle and the prototype yogic base
h- Dovzhina visoti, lowered from the top of the tricot tricycle to the base
Importantly... To brutalize respect for the signified wintry! Do not mix up α і β, and also aі b!
Note... Tse part of the lesson iz zavdannyi z geometrії (divided the area of the tricot tricycle). There is a change of staff, as the victories are difficult for the hour of the date. If you need to update the geometrical problem, there is no way to write about it at the forum. For the designation of the square root, at the problem connections, the symbol √ or sqrt () is used, and at the arches it is meant to be viraz.
Zavdannya
The bichna side of the tricot tricycle is 13 cm long, and the base is 10 cm long. Know the area tricycle tricycle.
Decision.
1st way... Zastosuєmo formula of Heron. Oskilki trikutnik ravnoedreniy, then there is more than a simple viglyad (div. Formula 1 in the list of formulas vishche): 
de a - dozhina of bichnyh parties, and b - dozhina of the basis.
Submitting the values of the tricycle side from the mind, we can recognize:
S = 1/2 * 10 * √ ((13 + 5) (13 - 5)) = 5 √ (18 * 8) = 60 cm 2
2nd way. Zastosuєmo Pythagoras' theorem
It is permissible that the formula is remembered by Vikoristan as the first method of solution. It is lowered from the vertex B to the base AC to the height of the BK.
Oskilki of the height of the femoral tricycle, cut the base of the navpil, then half of the base will be equal
AK = AC / 2 = 10/2 = 5 cm.
Hanging with a half of the base and side of the tricot tricycle will fix the rectangular tricycle ABK. We have a hypotenuse AB and a leg AK for a tricycle. Virazimo adjusting the other leg through the Pyfagorian theorem.