The perimeter of the rectangle is what is equal to the amount. What is a perimeter? What is a rectangle area

In this lesson, we will get acquainted with a new concept - the perimeter of the rectangle. We will formulate the definition of this concept, withdraw the formula to calculate it. We will also repeat the combination law of addition and the distribution law of multiplication.

On the this lesson We will get acquainted with the perimeter of the rectangle and its calculation.

Consider the following geometric shape (Fig. 1):

Fig. 1. Rectangle

This figure is a rectangle. Recall what distinctive features Rectangle we know.

The rectangle is a quadrangle, who has four straight corners and partially equal side.

That in our life can have rectangular shape? For example, a book, a table cover or a land plot.

Consider the following task:

Task 1 (Fig. 2)

Around land plot Builders needed to put a fence. The width of this plot is 5 meters, length - 10 meters. The fence is what length will be from builders?

Fig. 2. Illustration for task 1

The fence put on the borders of the site, so to find out the length of the fence, you need to know the length of each part. This rectangle has the parties: 5 meters, 10 meters, 5 meters, 10 meters. We will make an expression to calculate the length of the fence: 5 + 10 + 5 + 10. We use movement law Additions: 5 + 10 + 5 + 10 \u003d 5 + 5 + 10 + 10. In this expression there are sums of the same terms (5 + 5 and 10 + 10). We replace the sum of the same terms of the works: 5 + 5 + 10 + 10 \u003d 5 · 2 + 10 · 2. Now we use the distribution law of multiplication relative to addition: 5 · 2 + 10 · 2 \u003d (5 + 10) · 2.

Find the value of the expression (5 + 10) · 2. First, perform an action in brackets: 5 + 10 \u003d 15. And then repeat the number 15 twice: 15 · 2 \u003d 30.

Answer: 30 meters.

Perimeter of rectangle - The sum of all his sides. Formula for counting perimeter rectangle:, Here a is the length of the rectangle, and B is the width of the rectangle. The sum of length and width is called half-reader. In order to get a perimeter from half aimetime, you need to increase it 2 times, that is, multiply by 2.

We use the rectangle perimeter formula and we will find the perimeter of the rectangle with the sides of 7 cm and 3 cm: (7 + 3) · 2 \u003d 20 (cm).

The perimeter of any figure is measured in linear units.

In this lesson, we became acquainted with the perimeter of the rectangle and the formula for its calculation.

The number of numbers and the amount of numbers is equal to the amount of products of a given number and each of the terms.

If the perimeter is the sum of the lengths of all sides of the shape, then the half-meter is the sum of the same length and one width. We find a half-meter, when we work according to the formula of finding the perimeter of the rectangle (when we perform the first action in brackets - (a + b)).

Bibliography

Alexandrova E.I. Mathematics. Grade 2. - M.: Drop, 2004.
Bashmakov M.I., Nefodeova M.G. Mathematics. Grade 2. - M.: Astrel, 2006.
Dorofeev G.V., Miraca T.I. Mathematics. Grade 2. - M.: Enlightenment, 2012.

Festival.1September.ru ().
Nsportal.ru ().
Math-Prosto.ru ().

Homework

Find a rectangle perimeter, which has a length of 13 meters, and the width is 7 meters.
Find a semi-meter of a rectangle if its length is 8 cm, and the width is 4 cm.
Find the perimeter of the rectangle if its half-version is 21 dm.

The rectangle possesses many distinctive features, based on which the rules for calculating its various numeric characteristics have been developed. So rectangle:

Flat geometric figure;
Quadrangle;
The figure in which the opposite directions are equal and parallel, all the corners are straight.

Perimeter is the total length of all sides of the shape.

Calculation of the perimeter of the rectangle is a pretty simple task.

All you need to know is the width and length of the rectangle. Since the rectangle has two equal lengths and two equal widths, only one side is measured.

The perimeter of the rectangle is equal to the double sum of the 2nd sides of the length and width.

P \u003d (a + b) 2, where a is the length of the rectangle, B is the width of the rectangle.

Also, the perimeter of the rectangle can be found using the sum of all sides.

P \u003d a + a + b + b, where the length of the rectangle, B is the width of the rectangle.

The perimeter of the square is the length of the side of the square, multiplied by 4.

P \u003d A 4, where A is the length of the side of the square.

Supplement: Finding Find Square and Perimeter Rectangles

The study program for grade 3 provides for the study of polygons and their features. In order to understand how to find the perimeter of the rectangle and the area, we will understand what is meant under these concepts.

Basic concepts

Being perimeter and square requires knowledge of some terms. These include:

Right angle. It is formed from 2 rays having general Beginning In the form of a point. When finding out the figures (grade 3), the straight angle is determined by the coal.
Rectangle. This is a quadrangle, all the angles of which are straight. Its parties are called long and width. As you know, the opposite sides of this figure are equal.
Square. It is a quadrangle, all sides of which are equal.

When familiarizing with polygons, their vertices may be called ABSD. In mathematics, it is customary to refer point in the drawings of the letters of the Latin alphabet. The title of the polygon lists all the vertices without skips, for example, the ABC triangle.

Calculation of perimeter

The perimeter of the polygon is the sum of all its sides. This value is indicated by the Latin letter P. The level of knowledge for the proposed examples is 3 class.

Task # 1: "Instruct a 3 cm rectangle and 4 cm long with ABCD vertices. Find the perimeter of the ABCD rectangle.

The formula will look like this: P \u003d AB + BC + CD + AD or P \u003d AB × 2 + BC × 2.

Answer: P \u003d 3 + 4 + 3 + 4 \u003d 14 (cm) or p \u003d 3 × 2 + 4 × 2 \u003d 14 (cm).

Task number 2: "How to find a perimeter rectangular triangle ABC if the sides values \u200b\u200bare 5, 4 and 3 cm? ".

Answer: P \u003d 5 + 4 + 3 \u003d 12 (cm).

Task # 3: "Find the perimeter of the rectangle, one side of which is 7 cm, and another 2 cm is longer."

Answer: P \u003d 7 + 9 + 7 + 9 \u003d 32 (cm).

Task # 4: "Swimming competitions took place in the pool, the perimeter of which is 120 m. How many meters flew the participant of the competition, if the basin width is 10 m?".

This task is the question of how to find the length of the pool. To solve, find the lengths of the sides of the rectangle. The width is known. The sum of the lengths of the two unknown parties should be 100 m. 120-10 × 2 \u003d 100. To find out the distance that the swimmer overcomed, you need to divide the result obtained by 2. 100: 2 \u003d 50.

Answer: 50 (m).

Calculation of Square

A more complex value is the area of \u200b\u200bthe figure. For its measurement use measurements. The standard among the measurements are squares.

Square Square Side 1 cm is 1 cm². Square decimeter is designated as DM², and square meter - m².

Application areas of units may be:

Smalls measure small objects, such as photos, textbooks, sheets of paper.
In DM² you can measure the geographic map, window glass, picture.
For measuring gender, apartments, land use m².

If you draw a 3 cm rectangle with a length and 1 cm wide and split into squares with a side of 1 cm, then 3 squares fit in it, and therefore its area will be 3 cm². If the rectangle is smashed into squares, we find the perimeter of the rectangle also without difficulty. In this case, it is 8 cm.

Another way to calculate the number of squares accompanied in the figure is the use of a palette. Draw a square with an area of \u200b\u200b1 dm² on a tank, which is 100 cm². Let's place tracker on the figure and consider the number of square centimeters in one row. After that, we find out the number of rows, and then moving the values. So, the area of \u200b\u200bthe rectangle is a product of its length and width.

Methods of comparing areas:

Approximately. Sometimes it is enough just to look at items, because in some cases the naked eye shows that one figure takes more space, such as a textbook lying on the table next to the penalty.
Overlay. If the figures coincide when applied, their square is equal. If one of them is fully placed inside the second, then its area is less. Places occupied by a notebook sheet and a page from the textbook can be compared by imposing them on each other.
By the number of measure. Figures when applied may not coincide, but have the same area. In this case, you can calculate the number of squares to which the figure is broken.
Numbers. Compared numerical values \u200b\u200bmeasured by the same measurement, for example, in m².

Example №1: "The seamstress sewed a baby blanket from square multicolored flaps. One alcohol 1 dm long, in a row of 5 pieces. How many decimamers of the tape will need a seam for the processing of the edges of the blanket, if the area is known 50 dm²? ".

To solve the task, you need to answer the question how to find the length of the rectangle. Next, we find the perimeter of the rectangle composed of squares. It is clear from the task that the width of the blanket is 5 dm, we calculate the length, separating 50 to 5, and we get 10 dm. Now find the perimeter of the rectangle with the sides 5 and 10. p \u003d 5 + 5 + 10 + 10 \u003d 30.

Answer: 30 (m).

Example №2: "The site discovered on the excavations where the ancient treasures may be. How many territory will have to be explored by scientists if the perimeter is known 18 m and the width of the rectangle is 3 m? ".

We define the length of the site by doing 2 actions. 18-3 × 2 \u003d 12. 12: 2 \u003d 6. The desired territory will also be 18 m² (6 × 3 \u003d 18).

Answer: 18 (m²).

Thus, knowing the formulas, calculate the area and the perimeter will not be difficult, and the above examples will help to practice in solving mathematical problems.

One of the basic concepts of mathematics is the perimeter of the rectangle. There are many tasks on this topic, when solving which it is not necessary without the perimeter formula and its calculation skills.

Basic concepts

The rectangle is a quadrangle, which has all the corners direct, and the opposite sides are pairwise equal and parallel. In our lives, many figures have a rectangle shape, for example, a table surface, a notebook, and so on.

Consider an example: According to the boundaries of the land, it is necessary to put a fence. In order to find out the length of each side need to be measured.

Fig. 1. Land plot of a rectangle.

The land plot has a party to a length of 2 m., 4 m., 2 m., 4 m. Because the overall to learn the length of the fence must be added to the lengths of all sides:

2 + 2 + 4 + 4 \u003d 2 · 2 + 4 · 2 \u003d (2 + 4) · 2 \u003d 12 m.

It is this value in the general case and is called a perimeter. Thus, to find the perimeter, it is necessary to fold all sides of the figure. For the designation of the perimeter, use the letter P.

For calculating perimeter rectangular Figure It is not necessary to separate it on rectangles, you need to measure the line (roulette) only all sides of this figure and find their sum.

The perimeter of the rectangle is measured in mm., See, m., Km and so on. If necessary, the data in the task is translated into the same measurement system.

The perimeter of the rectangle is measured in various units: mm., See, m., Km and so on. If necessary, the data in the task is translated into one measurement system.

Formula perimeter Figure

If you take to your attention the fact that the opposite sides of the rectangle are equal, then you can withdraw the formula of the perimeter of the rectangle:

$ P \u003d (a + b) * $ 2, where a, b - side of the figure.

Fig. 2. Rectangle, with designated opposite sides.

There is another way to find a perimeter. If the task is given only one side and the area of \u200b\u200bthe figure, you can use the other side through the area. Then the formula will look like this:

$ P \u003d ((2S + 2A2) \\ OVER (A)) $, where S is the area of \u200b\u200bthe rectangle.

Fig. 3. Rectangle with sides A, b.

The task : Calculate the perimeter of the rectangle if its parties are 4 cm. And 6 cm.

Decision:

We use the formula $ p \u003d (a + b) * $ 2

$ P \u003d (4 + 6) * 2 \u003d 20 cm $

Thus, the perimeter of the figure is $ p \u003d 20 cm $.

Since the perimeter is the sum of all sides of the shape, then the half-version is the sum of only one length and width. To get the perimeter, it is necessary to multiply a half-period.

The area and perimeter are two basic concepts of measuring any figure. They cannot be confused, even though they are interconnected. If you increase, or reduce the area, then, accordingly, its perimeter will increase.

What did we know?

We learned how to find a perimeter of a rectangle. And also got acquainted with the formula for its calculation. With this topic, it is possible to encounter not only when solving mathematical problems, but also in real life.

Test on the topic

Evaluation of the article

Average rating: 4.5. Total ratings received: 373.

Class: 2

Purpose: Get acquainted with the reception of the perimeter of the rectangle.

Tasks:to form the ability to solve problems associated with finding the perimeter of the figures, develop skills to draw geometric shapes, consolidate the ability to calculate, applying with a moving property of addition, develop an oral account skill, logical thinking, to educate cognitive activity and the ability to work in the team.

Equipment:ICT (multimedia projector, presentation to the lesson), pictures with geometric shapes for fizminutka, model of the magic square, for students - models of geometric shapes, marker boards, rules, textbooks, notebooks.

DURING THE CLASSES

1. Organizational moment

Check availability to the lesson. Greeting.

The lesson begins,
He will go guys in the future.
Try to understand everything -
And carefully read.

2. Oral account

a) The use of magic figures. ( Attachment 1 )

- Fill the cells of the magic square, name it features (the amount of numbers horizontally, verticals and diagonals are equal to) and determine the magic number. (39)

In the chain, children fill the square on the board and in notebooks.

b) acquaintance with the properties of magic triangles. ( Appendix 2. )

- The sums of numbers in the corners forming the triangle are equal. Find the magic numbers in the triangle. Determine the missed number. Mark it on a marker board.

3. Preparation for the study of new material

- Before you geometric shapes. Name them in one word. (Quadriclers).
- divide them into 2 groups. ( Appendix 3. )
- What are rectangles. (Rectangles are quadrangles, who have all the corners direct.)
- What can I know, knowing the length of the sides of the quadricles? Perimeter - the sum of the side of the sides of the figures.
- Find the perimeter of a white figure, yellow.
- Why are the rectangles know not all parties?
- What are the properties of the opposite sides of the rectangles? (At the rectangle the opposite parties are equal).
- If the opposite sides are equal, is it necessary to measure all parties? (Not.)
- That's right enough to measure the length and width.
- How to calculate in a convenient way? (Students work orally with commenting.)

4. Study new topic

- Read the topic of our lesson: "Rectangle Perimeter". ( Appendix 4. )
- Help find the perimeter of this figure if its length is equal - but, and width - in.

Those who want to find the board. Students in notebooks write down the decision.

- How to write it differently?

P \u003d. but + but + in + in,
P \u003d. but x 2 +. in x 2
P \u003d ( but + in) x 2.

- We got a formula for finding the perimeter of the rectangle. ( Appendix 5. )

5. Fastening

P. 44 № 2.

Children read and write down the condition, the question drawn the figure, find p in different ways, write the answer.

6. Fizminutka. Signal Cards

How many green cells,
So much perform slopes.
So many times with clateers.
So many times with football legs.
How many cramps here are
So much let's jump.
We will come together as many times
So tighten now.

7. Practical work

- On your desks lie in the envelopes geometric shapes. How do we call them?
- What are rectangles?
- What do you know about opposite sides of rectangles?
- Measure the sides of the figures by options, find the perimeter in different ways.
- Check from a neighbor.

Multi-test notebooks.

- Read: How did you find the perimeter? What can be said about the perimeters of these figures? (They are equal).
- Instruct the rectangle with the same P, but other parties.

P 1 \u003d (2 + 6) x 2 \u003d 16 p 1 \u003d 2 x 2 + 6 x 2 \u003d 16
P 1 \u003d 2 + 2 + 6 + 6 \u003d 16
P 2 \u003d 3 + 3 + 5 + 5 \u003d 16 p 2 \u003d (3 + 5) x 2 \u003d 16
P 3 \u003d 4 + 4 + 4 + 4 \u003d 16 p 4 \u003d 1 + 1 + 7 + 7 \u003d 16

8. Graphic dictation

Left 6 cells. Put a point. We start moving. 2 - right, 4 - right down, 10 - left, 4 - right upwards. What figure? Turn it into a rectangle. Full. Find p in different ways.

P \u003d (5 + 2) x 2 \u003d 14.
P \u003d 5 + 5 + 2 + 2 \u003d 14.
P \u003d 5 x 2 + 2 x 2 \u003d 14.

9. Fingering gymnastics

Moved, multiplied.
Very, we are very tired.
Our fingers we rush and connect the palm.
And then, as soon as we can, firmly squeeze.
On the doors hanging the castle.
Who could not open it?
We knocked the lock,
We are castle castors,
We shouted the lock and opened.

(Words are accompanied by movements)

10. Drawing up and solving the problem of condition(Appendix 8. )

Rectangle length - 12 dm
Width - 3 dm m.
R - ?
In the first action, find the width: 12 - 3 \u003d 9 (dm) - width
Knowing the length and width, we will learn in one of the ways.
P \u003d (12 + 9) x 2 \u003d 42 dm

11. Independent work

12. Total lesson

- What was studied. How did you find a rectangle?

13. Postage

Answers are evaluated by students at the board and selectively in the process of independent work.

14. Easter task

P. 44 No. 5 (with explanations).

In this lesson, we will get acquainted with the perimeter of the rectangle and its calculation.

Consider the following geometric shape (Fig. 1):

Fig. 1. Rectangle

This figure is a rectangle. Recall what distinguishing features of the rectangle we know.

The rectangle is a quadrangle, who has four straight corners and partially equal side.

What in our life can have a rectangular shape? For example, a book, a table cover or a land plot.

Consider the following task:

Task 1 (Fig. 2)

Around the land plot, it was necessary to put a fence. The width of this plot is 5 meters, length - 10 meters. The fence is what length will be from builders?

Fig. 2. Illustration for task 1

The fence put on the borders of the site, so to find out the length of the fence, you need to know the length of each part. This rectangle has the parties: 5 meters, 10 meters, 5 meters, 10 meters. We will make an expression to calculate the length of the fence: 5 + 10 + 5 + 10. We use the prolonged law of addition: 5 + 10 + 5 + 10 \u003d 5 + 5 + 10 + 10. In this expression there are sums of the same terms (5 + 5 and 10 + 10). We replace the sum of the same terms of the works: 5 + 5 + 10 + 10 \u003d 5 · 2 + 10 · 2. Now we use the distribution law of multiplication relative to addition: 5 · 2 + 10 · 2 \u003d (5 + 10) · 2.

Find the value of the expression (5 + 10) · 2. First, perform an action in brackets: 5 + 10 \u003d 15. And then repeat the number 15 twice: 15 · 2 \u003d 30.

Answer: 30 meters.

We use the rectangle perimeter formula and we will find the perimeter of the rectangle with the sides of 7 cm and 3 cm: (7 + 3) · 2 \u003d 20 (cm).

The perimeter of any figure is measured in linear units.

In this lesson, we became acquainted with the perimeter of the rectangle and the formula for its calculation.

The number of numbers and the amount of numbers is equal to the amount of products of a given number and each of the terms.

Bibliography

Alexandrova E.I. Mathematics. Grade 2. - M.: Drop, 2004.
Bashmakov M.I., Nefodeova M.G. Mathematics. Grade 2. - M.: Astrel, 2006.
Dorofeev G.V., Miraca T.I. Mathematics. Grade 2. - M.: Enlightenment, 2012.

Festival.1September.ru ().
Nsportal.ru ().
Math-Prosto.ru ().

Homework

Find a rectangle perimeter, which has a length of 13 meters, and the width is 7 meters.
Find a semi-meter of a rectangle if its length is 8 cm, and the width is 4 cm.
Find the perimeter of the rectangle if its half-version is 21 dm.