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1 square decimeter is equal to 10 square centimeters. Unit of area - square decimeter

In this lesson, students are given the opportunity to get acquainted with another unit of measurement of area, the square decimeter, and learn how to translate square decimeters V square centimeters, and also practice performing various tasks to compare quantities and solve problems on the topic of the lesson.

Read the topic of the lesson: “The unit of area is the square decimeter.” In this lesson we will get acquainted with another unit of area, the square decimeter, and learn how to convert square decimeters into square centimeters and compare values.

Draw a rectangle with sides 5 cm and 3 cm and label its vertices with letters (Fig. 1).

Rice. 1. Illustration for the problem

Let's find the area of ​​the rectangle. To find the area, you need to multiply the length by the width of the rectangle.

Let's write down the solution.

5*3 = 15 (cm 2)

Answer: the area of ​​the rectangle is 15 cm 2.

We calculated the area of ​​this rectangle in square centimeters, but sometimes, depending on the problem being solved, the units of measurement of area may be different: more or less.

The area of ​​a square whose side is 1 dm is the unit of area, square decimeter(Fig. 2) .

Rice. 2. Square decimeter

The words “square decimeter” with numbers are written as follows:

5 dm 2, 17 dm 2

Let's establish the relationship between square decimeter and square centimeter.

Since a square with a side of 1 dm can be divided into 10 strips, each of which is 10 cm 2, then there are ten tens, or one hundred square centimeters in a square decimeter (Fig. 3).

Rice. 3. One hundred square centimeters

Let's remember.

1 dm 2 = 100 cm 2

Express these values ​​in square centimeters.

5 dm 2 = ... cm 2

8 dm 2 = ... cm 2

3 dm 2 = ... cm 2

Let's think like this. We know that there are one hundred square centimeters in one square decimeter, which means that there are five hundred square centimeters in five square decimeters.

Test yourself.

5 dm 2 = 500 cm 2

8 dm 2 = 800 cm 2

3 dm 2 = 300 cm 2

Express these values ​​in square decimeters.

400 cm 2 = ... dm 2

200 cm 2 = ... dm 2

600 cm 2 = ... dm 2

We explain the solution. One hundred square centimeters equals one square decimeter, which means that there are four square decimeters in 400 cm2.

Test yourself.

400 cm 2 = 4 dm 2

200 cm 2 = 2 dm 2

600 cm 2 = 6 dm 2

Follow the steps.

23 cm 2 + 14 cm 2 = ... cm 2

84 dm 2 - 30 dm 2 =… dm 2

8 dm 2 + 42 dm 2 = ... dm 2

36 cm 2 - 6 cm 2 = ... cm 2

Let's look at the first expression.

23 cm 2 + 14 cm 2 = ... cm 2

Fold numeric values: 23 + 14 = 37 and assign the name: cm 2. We continue to reason in a similar way.

Test yourself.

23 cm 2 + 14 cm 2 = 37 cm 2

84dm 2 - 30 dm 2 = 54 dm 2

8dm 2 + 42 dm 2 = 50 dm 2

36 cm 2 - 6 cm 2 = 30 cm 2

Read and solve the problem.

Mirror height rectangular shape- 10 dm, and width - 5 dm. What is the area of ​​the mirror (Fig. 4)?

Rice. 4. Illustration for the problem

To find out the area of ​​a rectangle, you need to multiply the length by the width. Let us pay attention to the fact that both quantities are expressed in decimeters, which means that the name of the area will be dm 2.

Let's write down the solution.

5 * 10 = 50 (dm 2)

Answer: mirror area - 50 dm2.

Compare the values.

20 cm 2 … 1 dm 2

6 cm 2 … 6 dm 2

95 cm 2…9 dm

It is important to remember: in order for quantities to be compared, they must have the same names.

Let's look at the first line.

20 cm 2 … 1 dm 2

Let's convert square decimeter to square centimeter. Remember that there are one hundred square centimeters in one square decimeter.

20 cm 2 … 1 dm 2

20 cm 2 … 100 cm 2

20 cm 2< 100 см 2

Let's look at the second line.

6 cm 2 … 6 dm 2

We know that square decimeters are larger than square centimeters, and the numbers for these names are the same, which means we put the sign “<».

6 cm 2< 6 дм 2

Let's look at the third line.

95cm 2…9 dm

Please note that area units are written on the left, and linear units on the right. Such values ​​cannot be compared (Fig. 5).

Rice. 5. Different sizes

Today in class we learned about another unit of area, the square decimeter, and learned how to convert square decimeters into square centimeters and compare values.

This concludes our lesson.

Bibliography

1. M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 1. - M.: “Enlightenment”, 2012.
2. M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 2. - M.: “Enlightenment”, 2012.
3. M.I. Moro. Mathematics lessons: Methodological recommendations for teachers. 3rd grade. - M.: Education, 2012.
4. Regulatory document. Monitoring and evaluation of learning outcomes. - M.: “Enlightenment”, 2011.
5. “School of Russia”: Programs for primary school. - M.: “Enlightenment”, 2011.
6. S.I. Volkova. Mathematics: Test work. 3rd grade. - M.: Education, 2012.
7. V.N. Rudnitskaya. Tests. - M.: “Exam”, 2012.

1. Nsportal.ru ().
2. Prosv.ru ().
3. Do.gendocs.ru ().

Homework

1. The length of the rectangle is 7 dm, the width is 3 dm. What is the area of ​​the rectangle?

2. Express these values ​​in square centimeters.

2 dm 2 = ... cm 2

4 dm 2 = ... cm 2

6 dm 2 = ... cm 2

8 dm 2 = ... cm 2

9 dm 2 = ... cm 2

3. Express these values ​​in square decimeters.

100 cm 2 = ... dm 2

300 cm 2 = ... dm 2

500 cm 2 = ... dm 2

700 cm 2 = ... dm 2

900 cm 2 = ... dm 2

4. Compare the values.

30 cm 2 ... 1 dm 2

7 cm 2 … 7 dm 2

81 cm 2 ...81 dm

5. Create an assignment for your friends on the topic of the lesson.

In this lesson, students are given the opportunity to become familiar with another unit of measurement of area, the square decimeter, learn how to convert square decimeters to square centimeters, and also practice performing various tasks on comparing quantities and solving problems on the topic of the lesson.

Read the topic of the lesson: “The unit of area is the square decimeter.” In this lesson we will get acquainted with another unit of area, the square decimeter, and learn how to convert square decimeters into square centimeters and compare values.

Draw a rectangle with sides 5 cm and 3 cm and label its vertices with letters (Fig. 1).

Rice. 1. Illustration for the problem

Let's find the area of ​​the rectangle. To find the area, you need to multiply the length by the width of the rectangle.

Let's write down the solution.

5*3 = 15 (cm 2)

Answer: the area of ​​the rectangle is 15 cm 2.

We calculated the area of ​​this rectangle in square centimeters, but sometimes, depending on the problem being solved, the units of measurement of area may be different: more or less.

The area of ​​a square whose side is 1 dm is the unit of area, square decimeter(Fig. 2) .

Rice. 2. Square decimeter

The words “square decimeter” with numbers are written as follows:

5 dm 2, 17 dm 2

Let's establish the relationship between square decimeter and square centimeter.

Since a square with a side of 1 dm can be divided into 10 strips, each of which is 10 cm 2, then there are ten tens, or one hundred square centimeters in a square decimeter (Fig. 3).

Rice. 3. One hundred square centimeters

Let's remember.

1 dm 2 = 100 cm 2

Express these values ​​in square centimeters.

5 dm 2 = ... cm 2

8 dm 2 = ... cm 2

3 dm 2 = ... cm 2

Let's think like this. We know that there are one hundred square centimeters in one square decimeter, which means that there are five hundred square centimeters in five square decimeters.

Test yourself.

5 dm 2 = 500 cm 2

8 dm 2 = 800 cm 2

3 dm 2 = 300 cm 2

Express these values ​​in square decimeters.

400 cm 2 = ... dm 2

200 cm 2 = ... dm 2

600 cm 2 = ... dm 2

We explain the solution. One hundred square centimeters equals one square decimeter, which means that there are four square decimeters in 400 cm2.

Test yourself.

400 cm 2 = 4 dm 2

200 cm 2 = 2 dm 2

600 cm 2 = 6 dm 2

Follow the steps.

23 cm 2 + 14 cm 2 = ... cm 2

84 dm 2 - 30 dm 2 =… dm 2

8 dm 2 + 42 dm 2 = ... dm 2

36 cm 2 - 6 cm 2 = ... cm 2

Let's look at the first expression.

23 cm 2 + 14 cm 2 = ... cm 2

We add up the numerical values: 23 + 14 = 37 and assign the name: cm 2. We continue to reason in a similar way.

Test yourself.

23 cm 2 + 14 cm 2 = 37 cm 2

84dm 2 - 30 dm 2 = 54 dm 2

8dm 2 + 42 dm 2 = 50 dm 2

36 cm 2 - 6 cm 2 = 30 cm 2

Read and solve the problem.

The height of the rectangular mirror is 10 dm, and the width is 5 dm. What is the area of ​​the mirror (Fig. 4)?

Rice. 4. Illustration for the problem

To find out the area of ​​a rectangle, you need to multiply the length by the width. Let us pay attention to the fact that both quantities are expressed in decimeters, which means that the name of the area will be dm 2.

Let's write down the solution.

5 * 10 = 50 (dm 2)

Answer: mirror area - 50 dm2.

Compare the values.

20 cm 2 … 1 dm 2

6 cm 2 … 6 dm 2

95 cm 2…9 dm

It is important to remember: in order for quantities to be compared, they must have the same names.

Let's look at the first line.

20 cm 2 … 1 dm 2

Let's convert square decimeter to square centimeter. Remember that there are one hundred square centimeters in one square decimeter.

20 cm 2 … 1 dm 2

20 cm 2 … 100 cm 2

20 cm 2< 100 см 2

Let's look at the second line.

6 cm 2 … 6 dm 2

We know that square decimeters are larger than square centimeters, and the numbers for these names are the same, which means we put the sign “<».

6 cm 2< 6 дм 2

Let's look at the third line.

95cm 2…9 dm

Please note that area units are written on the left, and linear units on the right. Such values ​​cannot be compared (Fig. 5).

Rice. 5. Different sizes

Today in class we learned about another unit of area, the square decimeter, and learned how to convert square decimeters into square centimeters and compare values.

This concludes our lesson.

Bibliography

1. M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 1. - M.: “Enlightenment”, 2012.
2. M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 2. - M.: “Enlightenment”, 2012.
3. M.I. Moro. Mathematics lessons: Methodological recommendations for teachers. 3rd grade. - M.: Education, 2012.
4. Regulatory document. Monitoring and evaluation of learning outcomes. - M.: “Enlightenment”, 2011.
5. “School of Russia”: Programs for primary school. - M.: “Enlightenment”, 2011.
6. S.I. Volkova. Mathematics: Test work. 3rd grade. - M.: Education, 2012.
7. V.N. Rudnitskaya. Tests. - M.: “Exam”, 2012.

1. Nsportal.ru ().
2. Prosv.ru ().
3. Do.gendocs.ru ().

Homework

1. The length of the rectangle is 7 dm, the width is 3 dm. What is the area of ​​the rectangle?

2. Express these values ​​in square centimeters.

2 dm 2 = ... cm 2

4 dm 2 = ... cm 2

6 dm 2 = ... cm 2

8 dm 2 = ... cm 2

9 dm 2 = ... cm 2

3. Express these values ​​in square decimeters.

100 cm 2 = ... dm 2

300 cm 2 = ... dm 2

500 cm 2 = ... dm 2

700 cm 2 = ... dm 2

900 cm 2 = ... dm 2

4. Compare the values.

30 cm 2 ... 1 dm 2

7 cm 2 … 7 dm 2

81 cm 2 ...81 dm

5. Create an assignment for your friends on the topic of the lesson.

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1 square decimeter [dm²] = 100 square centimeter [cm²]

Initial value

Converted value

square meter square kilometer square hectometer square decameter square decimeter square centimeter square millimeter square micrometer square nanometer hectare ar barn square mile sq. mile (US, surveyor) square yard square foot² sq. foot (USA, surveyor) square inch circular inch township section acre acre (USA, surveyor) ore square chain square rod rod² (USA, surveyor) square perch square rod sq. thousandth circular mil homestead sabin arpan cuerda square castilian cubit varas conuqueras cuad cross section of electron tithe (government) tithe economic round square verst square arshin square foot square fathom square inch (Russian) square line Planck area

More about the area

General information

Area is the size of a geometric figure in two-dimensional space. It is used in mathematics, medicine, engineering and other sciences, for example in calculating the cross-section of cells, atoms, or pipes such as blood vessels or water pipes. In geography, area is used to compare the sizes of cities, lakes, countries, and other geographic features. Population density calculations also use area. Population density is defined as the number of people per unit area.

Units

Square meters

Area is measured in SI units in square meters. One square meter is the area of ​​a square with a side of one meter.

Unit square

A unit square is a square with sides of one unit. The area of ​​a unit square is also equal to one. In a rectangular coordinate system, this square is located at coordinates (0,0), (0,1), (1,0) and (1,1). On the complex plane the coordinates are 0, 1, i And i+1, where i- imaginary number.

Ar

Ar or weaving, as a measure of area, is used in the CIS countries, Indonesia and some other European countries, to measure small urban objects such as parks, when a hectare is too large. One are is equal to 100 square meters. In some countries this unit is called differently.

Hectare

Real estate, especially land, is measured in hectares. One hectare is equal to 10,000 square meters. It has been in use since the French Revolution, and is used in the European Union and some other regions. Just like the macaw, in some countries the hectare is called differently.

Acre

In North America and Burma, area is measured in acres. The hectares are not used there. One acre is equal to 4046.86 square meters. An acre was originally defined as the area that a farmer with a team of two oxen could plow in one day.

Barn

Barns are used in nuclear physics to measure the cross section of atoms. One barn is equal to 10⁻²⁸ square meters. The barn is not a unit in the SI system, but is accepted for use in this system. One barn is approximately equal to the cross-sectional area of ​​a uranium nucleus, which physicists jokingly called “as huge as a barn.” Barn in English is “barn” (pronounced barn) and from a joke among physicists this word became the name of a unit of area. This unit originated during World War II, and was liked by scientists because its name could be used as a code in correspondence and telephone conversations within the Manhattan Project.

Area calculation

The area of ​​the simplest geometric figures is found by comparing them with the square of a known area. This is convenient because the area of ​​the square is easy to calculate. Some formulas for calculating the area of ​​geometric figures given below were obtained in this way. Also, to calculate the area, especially of a polygon, the figure is divided into triangles, the area of ​​each triangle is calculated using the formula, and then added. The area of ​​more complex figures is calculated using mathematical analysis.

Formulas for calculating area

• Square: square side.
• Rectangle: product of the parties.
• Triangle (side and height known): the product of the side and the height (the distance from this side to the edge), divided in half. Formula: A = ½ah, Where A- square, a- side, and h- height.
• Triangle (two sides and the angle between them are known): the product of the sides and the sine of the angle between them, divided in half. Formula: A = ½ab sin(α), where A- square, a And b- sides, and α - the angle between them.
• Equilateral triangle: side squared divided by 4 and multiplied by the square root of three.
• Parallelogram: the product of a side and the height measured from that side to the opposite side.
• Trapezoid: the sum of two parallel sides multiplied by the height and divided by two. The height is measured between these two sides.
• Circle: the product of the square of the radius and π.
• Ellipse: product of semi-axes and π.

Surface Area Calculation

You can find the surface area of ​​simple volumetric figures, such as prisms, by unfolding this figure on a plane. It is impossible to obtain a development of the ball in this way. The surface area of ​​a sphere is found using the formula by multiplying the square of the radius by 4π. From this formula it follows that the area of ​​a circle is four times less than the surface area of ​​a ball with the same radius.

Surface areas of some astronomical objects: Sun - 6,088 x 10¹² square kilometers; Earth - 5.1 x 10⁸; thus, the surface area of ​​the Earth is approximately 12 times smaller than the surface area of ​​the Sun. The Moon's surface area is approximately 3.793 x 10⁷ square kilometers, which is about 13 times smaller than the Earth's surface area.

Planimeter

The area can also be calculated using a special device - a planimeter. There are several types of this device, for example polar and linear. Also, planimeters can be analog and digital. In addition to other functions, digital planimeters can be scaled, making it easier to measure features on a map. The planimeter measures the distance traveled around the perimeter of the object being measured, as well as the direction. The distance traveled by the planimeter parallel to its axis is not measured. These devices are used in medicine, biology, technology, and agriculture.

Theorem on properties of areas

According to the isoperimetric theorem, of all figures with the same perimeter, the circle has the largest area. If, on the contrary, we compare figures with the same area, then the circle has the smallest perimeter. The perimeter is the sum of the lengths of the sides of a geometric figure, or the line that marks the boundaries of this figure.

Geographical features with the largest area

Country: Russia, 17,098,242 square kilometers, including land and water. The second and third largest countries by area are Canada and China.

City: New York is the city with the largest area of ​​8683 square kilometers. The second largest city by area is Tokyo, occupying 6993 square kilometers. The third is Chicago, with an area of ​​5,498 square kilometers.

City Square: The largest square, covering 1 square kilometer, is located in the capital of Indonesia, Jakarta. This is Medan Merdeka Square. The second largest area, at 0.57 square kilometers, is Praça doz Girascoes in the city of Palmas, Brazil. The third largest is Tiananmen Square in China, 0.44 square kilometers.

Lake: Geographers debate whether the Caspian Sea is a lake, but if so, it is the largest lake in the world with an area of ​​371,000 square kilometers. The second largest lake by area is Lake Superior in North America. It is one of the lakes of the Great Lakes system; its area is 82,414 square kilometers. The third largest lake in Africa is Lake Victoria. It covers an area of ​​69,485 square kilometers.

metric unit of area = 0.01 square meter = 100 sq. centimeters = 15.50 sq. inches = 5.061 sq. top; The abbreviated designation for square decimeter legalized in the USSR: Russian - “dm 2”, or “sq. dm”, Latin - “dm2”.

• - linear measure of the metric system = 0.1 meters = 10 centimeters = 3.937 inches - 2.2497 vershok; The abbreviation a, legalized in the USSR: Russian - “dm”, Latin - “dm”...

  Reference commercial dictionary

• -) a tenth of a meter...

  Great Soviet Encyclopedia

• - a tenth of a meter, denoted...

  Large encyclopedic dictionary

• - ; pl. decime/three, R....
• - ...

  Spelling dictionary of the Russian language

• - decime/tr,...

  Together. Apart. Hyphenated. Dictionary-reference book

• - DECIMETER, husband. A unit of measurement equal to one tenth of a meter. | adj. decimeter, -aya, -oh. Decimeter radio waves...

  Ozhegov's Explanatory Dictionary

• - SQUARE, -aya, -oe; -ten, -tna. 1. see square. 2. full Shaped like a square; like a square. K. table. Square brackets. 3. Shaped like a square. K. chin. Square shoulders...

  Ozhegov's Explanatory Dictionary

• - SQUARE, square, square. 1. adj. to a square of 4 digits. . Square measures. Square meter. Square root. Quadratic equation. 2. Shaped like a square. Square item...

  Ushakov's Explanatory Dictionary

• - decimeter m. A unit of length equal to one tenth of a meter...

  Explanatory Dictionary by Efremova

• - square I adj. 1. ratio with noun square I, associated with it 2. Peculiar to the square, characteristic of it. 3. Shaped like a square. II adj. 1. ratio with noun square III associated with it; quadratic 1.. 2...

  Explanatory Dictionary by Efremova

• - ...

  Spelling dictionary-reference book

• - decim "...

  Russian spelling dictionary

• - DECIMETER a, m. décimètre m. French unit of length, one tenth of a metre. Jan. 1803 1 694. A unit of length equal to one tenth of a meter. BAS-2. Decimeter. 1831. Petrushevsky 321...

  Historical Dictionary of Gallicisms of the Russian Language

• - See DESIMETER...

  Dictionary of foreign words of the Russian language

• - ...

  Word forms

"square decimeter" in books

Nuss broit (square bread)

From the book All about Jewish cuisine author Rosenbaum (compiler) Gennady

Square root of two = 1.414...

author Prokopenko Iolanta

The square root of two = 1.414... And every part of the city has four sides, And every inhabitant too, And every pot, and vessel, and clothing, and utensils of the houses, And every house has four walls. William Blake, English poet and artist, mystic and visionary In sacred geometry

Square root of five = 2.236

From the book Sacred Geometry. Energy codes of harmony author Prokopenko Iolanta

Square root of five = 2.236 The Pythagoreans revered the number 5 as sacred. It is directly related to the concept of the golden ratio. The golden ratio is the arithmetic mean of 1 and the root of 5. ?5/2 is the diagonal of half a square, is a geometric

24. Square circle

From the book The Pig Who Wanted to Be Eaten author Bajini Julian

24. Square circle And God said to the philosopher: “I am the Lord your God, I am omnipotent. Anything you say can be done. It’s easy!” And the philosopher answered God: “Okay, Your Omnipotence. Make everything blue red and everything red blue.” And God said: “Let the colors change places!” AND

Semi-dug square pool

From the book Modern outbuildings and site development author Nazarova Valentina Ivanovna

Semi-dug square pool To begin with, we will describe in detail the technological operations of constructing a pool measuring 2.5x2.5 m on a site. The pool is semi-dug, which means that excavation work awaits. A pit is dug 2.5x2.5 m, 0.6 m deep. Make drainage immediately. This

4.4. "Square Man"

From the book Art and Beauty in Medieval Aesthetics by Eco Umberto

4.4. “Square Man” However, along with this naturalistic cosmology, in the same 12th century, another aspect of Pythagorean cosmology was developed in great detail - we are talking about the resuscitation and unification of traditional motifs associated with the square man (homo quadratus).

Square cover with buttons

From the book Pillow Toys author Boyko Elena Anatolyevna

Square cover with buttons To make a square cover you will need 3 buttons with a diameter of 1.2 cm (you can use buttons covered with fine-checked shirt fabric), sewing threads corresponding to the color and thickness of the fabric used, paper and a pencil.

Decimeter

From the book Great Soviet Encyclopedia (DE) by the author TSB

20. Quadratic Trinomial, or Algebraic Calculation Package

From the book Sketches for Programmers [incomplete, chapters 1–24] by Wetherell Charles

20. Quadratic Trinomial, or Algebraic Calculus Package The main difficulty that a programmer faces in most programming languages ​​is the need to break down his equations into small parts when writing calculations. Yes, if required

154. Square meter

From the book Fun Problems. Two hundred puzzles author Perelman Yakov Isidorovich

154. Square meter I knew a schoolboy who, having heard for the first time that there are a million square millimeters in a square meter, did not want to believe it. No explanation was convincing to him. “Where do so many of them come from? - he was perplexed. - Here I have a sheet of millimeter paper.

100. Square meter

author Perelman Yakov Isidorovich

100. Square meter When Alyosha heard for the first time that a square meter contains a million square millimeters, he did not want to believe it. - Where do so many of them come from? - he was surprised. - Here I have a sheet of graph paper exactly a meter long and wide. So

100. Square meter

From the book Scientific Tricks and Riddles author Perelman Yakov Isidorovich

100. Square meter On the same day, Alyosha could not be sure of this. Even if he counted continuously around the clock, even then he would count only 86,400 cells in one day. After all, there are only 86,400 seconds in 24 hours. He would have to count more than ten days without interruption, but

Square Forehead The square shape of the forehead is determined by the direction of the hairline straight up from the temples, and then the same straight line parallel to the eyebrows. The forehead looks like a square or rectangle (Fig. 3.6). Such people, like people with a trapezoidal forehead, are prone to

In this lesson, students are given the opportunity to become familiar with another unit of measurement of area, the square decimeter, learn how to convert square decimeters to square centimeters, and also practice performing various tasks on comparing quantities and solving problems on the topic of the lesson.

Read the topic of the lesson: “The unit of area is the square decimeter.” In this lesson we will get acquainted with another unit of area, the square decimeter, and learn how to convert square decimeters into square centimeters and compare values.

Draw a rectangle with sides 5 cm and 3 cm and label its vertices with letters (Fig. 1).

Rice. 1. Illustration for the problem

Let's find the area of ​​the rectangle. To find the area, you need to multiply the length by the width of the rectangle.

Let's write down the solution.

5*3 = 15 (cm 2)

Answer: the area of ​​the rectangle is 15 cm 2.

We calculated the area of ​​this rectangle in square centimeters, but sometimes, depending on the problem being solved, the units of measurement of area may be different: more or less.

The area of ​​a square whose side is 1 dm is the unit of area, square decimeter(Fig. 2) .

Rice. 2. Square decimeter

The words “square decimeter” with numbers are written as follows:

5 dm 2, 17 dm 2

Let's establish the relationship between square decimeter and square centimeter.

Since a square with a side of 1 dm can be divided into 10 strips, each of which is 10 cm 2, then there are ten tens, or one hundred square centimeters in a square decimeter (Fig. 3).

Rice. 3. One hundred square centimeters

Let's remember.

1 dm 2 = 100 cm 2

Express these values ​​in square centimeters.

5 dm 2 = ... cm 2

8 dm 2 = ... cm 2

3 dm 2 = ... cm 2

Let's think like this. We know that there are one hundred square centimeters in one square decimeter, which means that there are five hundred square centimeters in five square decimeters.

Test yourself.

5 dm 2 = 500 cm 2

8 dm 2 = 800 cm 2

3 dm 2 = 300 cm 2

Express these values ​​in square decimeters.

400 cm 2 = ... dm 2

200 cm 2 = ... dm 2

600 cm 2 = ... dm 2

We explain the solution. One hundred square centimeters equals one square decimeter, which means that there are four square decimeters in 400 cm2.

Test yourself.

400 cm 2 = 4 dm 2

200 cm 2 = 2 dm 2

600 cm 2 = 6 dm 2

Follow the steps.

23 cm 2 + 14 cm 2 = ... cm 2

84 dm 2 - 30 dm 2 =… dm 2

8 dm 2 + 42 dm 2 = ... dm 2

36 cm 2 - 6 cm 2 = ... cm 2

Let's look at the first expression.

23 cm 2 + 14 cm 2 = ... cm 2

We add up the numerical values: 23 + 14 = 37 and assign the name: cm 2. We continue to reason in a similar way.

Test yourself.

23 cm 2 + 14 cm 2 = 37 cm 2

84dm 2 - 30 dm 2 = 54 dm 2

8dm 2 + 42 dm 2 = 50 dm 2

36 cm 2 - 6 cm 2 = 30 cm 2

Read and solve the problem.

The height of the rectangular mirror is 10 dm, and the width is 5 dm. What is the area of ​​the mirror (Fig. 4)?

Rice. 4. Illustration for the problem

To find out the area of ​​a rectangle, you need to multiply the length by the width. Let us pay attention to the fact that both quantities are expressed in decimeters, which means that the name of the area will be dm 2.

Let's write down the solution.

5 * 10 = 50 (dm 2)

Answer: mirror area - 50 dm2.

Compare the values.

20 cm 2 … 1 dm 2

6 cm 2 … 6 dm 2

95 cm 2…9 dm

It is important to remember: in order for quantities to be compared, they must have the same names.

Let's look at the first line.

20 cm 2 … 1 dm 2

Let's convert square decimeter to square centimeter. Remember that there are one hundred square centimeters in one square decimeter.

20 cm 2 … 1 dm 2

20 cm 2 … 100 cm 2

20 cm 2< 100 см 2

Let's look at the second line.

6 cm 2 … 6 dm 2

We know that square decimeters are larger than square centimeters, and the numbers for these names are the same, which means we put the sign “<».

6 cm 2< 6 дм 2

Let's look at the third line.

95cm 2…9 dm

Please note that area units are written on the left, and linear units on the right. Such values ​​cannot be compared (Fig. 5).

Rice. 5. Different sizes

Today in class we learned about another unit of area, the square decimeter, and learned how to convert square decimeters into square centimeters and compare values.

This concludes our lesson.

Bibliography

1. M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 1. - M.: “Enlightenment”, 2012.
2. M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 2. - M.: “Enlightenment”, 2012.
3. M.I. Moro. Mathematics lessons: Methodological recommendations for teachers. 3rd grade. - M.: Education, 2012.
4. Regulatory document. Monitoring and evaluation of learning outcomes. - M.: “Enlightenment”, 2011.
5. “School of Russia”: Programs for primary school. - M.: “Enlightenment”, 2011.
6. S.I. Volkova. Mathematics: Test work. 3rd grade. - M.: Education, 2012.
7. V.N. Rudnitskaya. Tests. - M.: “Exam”, 2012.

1. Nsportal.ru ().
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3. Do.gendocs.ru ().

Homework

1. The length of the rectangle is 7 dm, the width is 3 dm. What is the area of ​​the rectangle?

2. Express these values ​​in square centimeters.

2 dm 2 = ... cm 2

4 dm 2 = ... cm 2

6 dm 2 = ... cm 2

8 dm 2 = ... cm 2

9 dm 2 = ... cm 2

3. Express these values ​​in square decimeters.

100 cm 2 = ... dm 2

300 cm 2 = ... dm 2

500 cm 2 = ... dm 2

700 cm 2 = ... dm 2

900 cm 2 = ... dm 2

4. Compare the values.

30 cm 2 ... 1 dm 2

7 cm 2 … 7 dm 2

81 cm 2 ...81 dm

5. Create an assignment for your friends on the topic of the lesson.