How to convert square decimeters to square centimeters. square decimeter

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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 survey) square yard square foot² sq. ft (US, survey) square inch circular inch township section acre acre (US, survey) ore square chain square rod² (US, survey) square perch square rod sq. thousandth circular mil homestead sabine arpan cuerda square castilian cubit varas conuqueras cuad electron cross-section tithe (official) household tithe round square verst square arshin square foot square sazhen square inch (Russian) square line Plank area

More about the square

General information

Area is the size of a geometric figure in two-dimensional space. It is used in mathematics, medicine, engineering, and other sciences, such as 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. Area is also used in population density calculations. 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 unity. In a rectangular coordinate system, this square is 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 is an imaginary number.

Ar

Ar or sotka, 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 is measured in hectares, especially land plots. 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. As well as ar, in some countries the hectare is called differently.

Acre

In North America and Burma, area is measured in acres. Hectares are not used there. One acre is equal to 4046.86 square meters. Initially, an acre was defined as the area that a peasant 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 equals 10⁻²⁸ square meters. 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 the uranium nucleus, which physicists jokingly called "huge as a barn." Barn in English "barn" (pronounced barn) and from a joke of physicists, this word became the name of a unit of area. This unit originated during World War II, and scientists liked it 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 a square is easy to calculate. Some formulas for calculating the area of geometric shapes below are obtained in this way. Also, to calculate the area, especially a polygon, the figure is divided into triangles, the area of \u200b\u200beach triangle is calculated using the formula, and then added. The area of more complex figures is calculated using mathematical analysis.

Area formulas

Square: square side.
Rectangle: product of the parties.
Triangle (side and height are known): the product of a side and the height (the distance from that 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 are the sides, and α is the angle between them.
Equilateral triangle: side, squared, divided by 4 times the square root of three.
Parallelogram: the product of a side and the height measured from that side to the opposite side.
Trapeze: the sum of two parallel sides multiplied by the height, divided by two. Height is measured between these two sides.
A circle: the product of the square of the radius and π.
Ellipse: product of semiaxes and π.

Surface area calculation

You can find the surface area of simple three-dimensional figures, such as prisms, by unfolding this figure on a plane. It is impossible to obtain a ball scan 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 about 12 times smaller than the surface area of the Sun. The surface area of the Moon is approximately 3.793 x 10⁷ square kilometers, which is about 13 times smaller than the surface area of the Earth.

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 are analog and digital. In addition to other features, digital planimeters can be scaled to make it easier to measure features on a map. The planimeter measures the distance traveled along the perimeter of the measured object, 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, engineering, and agriculture.

Area properties theorem

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 a line that marks the boundaries of this figure.

Geographic features with the largest area

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

City: New York is the city with the largest area at 8,683 square kilometers. The second largest city is Tokyo, covering 6,993 square kilometers. The third is Chicago, with an area of 5498 square kilometers.

City Square: The largest area, 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 dos Giraçois in the city of Palmas, in Brazil. The third largest is Tiananmen Square in China, 0.44 square kilometers.

Lake: Geographers argue whether the Caspian Sea is a lake, but if it is, then it is the largest lake in the world with an area of 371,000 square kilometers. The second largest lake 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 is Lake Victoria in Africa. It covers an area of 69,485 square kilometers.

Lesson Objectives: introduce students to a new unit of area measurement - a square decimeter.

Tasks:

Introduce the concept of "square decimeter", give an idea about the use of a new unit of measurement, its relationship with a square centimeter.
Develop logical thinking, attention, memory, observation; Computing skills; the ability to measure length and area.
To cultivate the ability to work in pairs, perseverance, accuracy.

DURING THE CLASSES

1. Message of the topic and purpose of the lesson

- To find out what we will work on today, complete the warm-up tasks. Find the extra one in each group and choose the corresponding letter.

P) 3, 5, 7
P) 16, 20, 24
C) 28, 32, 36

K) 5 + 5 + 5
L) 5 + 23 + 8
M) 23 + 23 + 8

3) Choose a solution to the problem: “36 titmouse flew to the feeder, 9 times less nuthatches. How many nuthatch flew in?

O) 36: 9
P) 36 - 9
R) 36 + 9

H) RECTANGLE
W) SQUARE
SCH) TRIANGLE

BUT) KG
B) MM
B) SM

D) (5 + 3) 2
D) (5 – 3) 2
E) 5 2 + 3 2

b) IN? MORE TIMES (x)
E) IN? MORE TIMES (:)
I AM IN? ONCE LESS (:)

- Read what word you got. (Square)
– Why do you think? (In previous lessons, we learned how to calculate the area of \u200b\u200bfigures)
- Let's continue this work and get acquainted with a new unit of area.
What area do we already know how to calculate?
What is the unit of measure for area.

II. Knowledge update

1) Math dictation

Calculate the product of numbers 4 and 8
Increase the number 8 by 6 times
Divide the number 40 by 4 times
From 14 m of fabric, the tailor sewed 7 identical suits. How many meters of fabric did each suit take?
What number must be multiplied by 3 to get 15.
What is the perimeter of a square whose side is 2 cm?
How many cm in 1 dm?
To repair the apartment, we bought 4 cans of paint, 3 kg each. How many kg of paint did you buy in total?

Answers: 32, 48, 10, 2m, 5, 8 cm, 10 cm, 12 kg.

What 2 groups can we divide our answers into? (Prime numbers and named; even and odd; single and double digits)
- Underline the named numbers. Among the named, name the odd one. (12 kg)

2) Value conversion

(Individual work at the blackboard is performed by 2 students)

- And now let's check how the students performed the transformation of named quantities

1 cm = ... mm
1 dm = ... cm
1 m = ... dm
65 cm = ... dm ... cm
27 mm = ... cm ... mm
8 m 9 dm = ... dm

What is measured in these units? (Length)
What other units of measurement do you know? (Area units)

3) Solving problems on finding the area of a rectangle and a square.

Figures on the board (rectangles and squares).

- Let's remember the formulas for finding the areas of these figures.

(One of the students comes out and chooses the necessary ones from the set of formulas for finding the perimeter and area for rectangles and squares).

S rectangle = a x b

S square = a x a

P square = a x 4

P rectangle = (a + b) x 2

What unit of area do you know? (cm 2)

What is a square centimeter? (This is a square whose side is 1 cm.)

- What is its area? (1 cm 2)

III. Update.

1) - Today we will continue to talk about the area of \u200b\u200ba rectangle and get acquainted with a new unit for measuring area, a new measure.

Divide the numbers into 2 groups:

3 cm
2 dm
46
4 mm
100
18 cm 2
2 dm 2
18

(Numbers can be divided into named numbers and ordinary numbers, numbers denoting length, area)

– Read units of area? (18 square centimeters, 2 square decimetres)
- What can be the sides of a rectangle with an area of 18 sq.cm? (2 cm and 9 cm, 6 cm and 3 cm, 18 cm and 1 cm)
What unit of area are we already familiar with? (Square centimeter).
- And what unit of area from the named ones have we not talked about in detail yet? (dm2)
- Try to formulate the topic of the lesson? (Let's get acquainted with the square decimeter)
– We will get acquainted with a square decimeter, find out how it is related to a square centimeter, we will learn to solve problems using a new unit of area
- But let's remember how to measure the area of a rectangle? (Divide into square centimeters using a palette; by overlaying figures; by applying a measure; measure the length and width and multiply the data).

2) Work in pairs

Now you will work in pairs. You have an envelope with figures on your desk. Take out the green rectangle from the envelope and find its area yourself.
- Let's remember what needs to be done for this? (Measure the length and width, multiply the length by the width)

3 x 4 = 12 sq. cm.

We have found the area of the rectangle. It is equal to 12 sq.cm. In what units do we measure the area of this rectangle? (In sq.cm).

IV. New topic

1) Getting to know the square decimeter

- Put the yellow rectangle in front of you and take out the small square from the envelope. What can you say about this square? (This is a measurement - 1 square centimeter)
Try using this measure to measure the area of a rectangle. How will you do it? (attach square)
What is the area of this rectangle? (didn't get to know)
- Why didn’t you have time, you have everything for measuring, you worked in pairs, what happened? (Small measure, and the rectangle is large, you need to lay it for a long time)
– There is another measure in the envelope, a large one, try to measure with this measure. (The measure fit 2 times)
Why did you complete this task so quickly? (The measure is large, it was easy to measure)
Now, use a ruler to measure the sides of the large measure. (10 cm)
- How else to write 10 cm? (1 dm)

- So a large measure is a square with a side of 1 dm. Look in your notebook at the little square you have drawn. Compare with large scale. Think and tell me how in mathematics we call a square with a side of 1 dm? (1 square decimeter).

2) Work with the textbook

– Read the explanation on page 14.
- Why did people need to use a new unit of measurement of 1 sq. dm, if they already had a unit of 1 sq. cm? (To make it easier to measure large shapes or objects)
- What do you think, the area of \u200b\u200bwhat can be measured in dm 2? (Square of a textbook, notebook, table, board).

3) Relationship between square dm and square cm.

- And let's calculate how many square centimeters fit in 1 square. dm. How can I do that? (Divide the large square by square cm and count; we know that the side of the large square is 10 cm, we can multiply 10 by 10).
- Some suggested dividing by square centimeters and counting. Let's try to do that.
Try to count quickly. What is the easier and faster way? (Multiply 10 by 10)
- Count. (100 sq. cm)

1 sq. dm = 100 sq.cm

So what have we learned now? (How sq. dm is related to sq. cm)

V. Physical education

VI. Anchoring

- Now we will learn to solve problems using a new unit of area.

1) Problem S. 14, No. 3

– The height of a rectangular mirror is 10 dm, and the width is 5 dm. What is the area of the mirror?
What units are used to measure the height and width of a mirror? (in dm)
- Why? (mirror large)

The student at the blackboard decides with an explanation.

2) Task p.14, No. 4 (Two students at the blackboard)

3) Solution of examples (Orally in a chain)

L - 9 x (38 - 30) \u003d M - 8 x 7 + 5 x 2 \u003d
O - 65 - (49 - 19) \u003d C - 9 x 9 + 28: 7 \u003d
D - 28 + 45: 5 \u003d N - 7 x (100 - 91) \u003d

VII. Lesson summary

Our lesson has come to an end.
What topic were you working on?
In what units is area measured?
– How many square cm are in 1 square DM?
– What new things have you learned for yourself?
- What did you enjoy doing the most?
- What were the difficulties?

VIII. Homework

- Repeat the new material, and consolidate the ability to find the area of rectangles - p.14, No. 2.

1 square meter [m²] = 100 square decimeter [dm²]

Initial value

Converted value

Ferrofluids

More about the square

General information

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

Ar

Hectare

Acre

barn

Area calculation

Area formulas

Square: square side.
Rectangle: product of the parties.
Triangle (side and height are known): the product of a side and the height (the distance from that 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 are the sides, and α is the angle between them.
Equilateral triangle: side, squared, divided by 4 times the square root of three.
Parallelogram: the product of a side and the height measured from that side to the opposite side.
Trapeze: the sum of two parallel sides multiplied by the height, divided by two. Height is measured between these two sides.
A circle: the product of the square of the radius and π.
Ellipse: product of semiaxes and π.

Surface area calculation

planimeter

Area properties theorem

Geographic features with the largest area

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

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

Read the topic of the lesson: "The unit of area is a square decimeter." In the lesson, we will get acquainted with another unit of area, a square decimeter, learn how to convert square decimeters to 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, multiply the length by the width of the rectangle.

Let's write down the solution.

5*3=15(cm2)

Answer: the area of a rectangle is 15 cm2.

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

The area of a square whose side is 1 dm is a 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 ratio between square decimeter and square centimeter.

Since a square with a side of 1 dm can be divided into 10 strips, each of which has 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 \u003d 100 cm 2

Express these values in square centimeters.

5 dm 2 \u003d ... cm 2

8 dm 2 = ... cm 2

3 dm 2 = ... cm 2

We reason 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 \u003d 500 cm 2

8 dm 2 \u003d 800 cm 2

3 dm 2 \u003d 300 cm 2

Express these quantities in square decimetres.

400 cm 2 = ... dm 2

200 cm 2 = ... dm 2

600 cm 2 = ... dm 2

We explain the solution. One hundred square centimeters make up one square decimeter, which means that in the number 400 cm 2 there are four square decimeters.

Test yourself.

400 cm 2 = 4dm 2

200 cm 2 \u003d 2 dm 2

600 cm 2 \u003d 6 dm 2

Take action.

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

84 dm 2 - 30 dm 2 \u003d ... dm 2

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

36 cm 2 - 6 cm 2 \u003d ... cm 2

Consider 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 the same way.

Test yourself.

23 cm 2 + 14 cm 2 \u003d 37 cm 2

84dm 2 - 30 dm 2 \u003d 54 dm 2

8dm 2 + 42 dm 2 = 50 dm 2

36 cm 2 - 6 cm 2 \u003d 30 cm 2

Read and solve the problem.

The height of a 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 the area of a rectangle, multiply the length by the width. Let's pay attention to the fact that both values 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: the mirror area is 50 dm 2.

Compare sizes.

20 cm 2 ... 1 dm 2

6 cm 2 ... 6 dm 2

95 cm 2 ... 9 dm

It is important to remember that in order for values to be compared, they must have the same name.

Let's look at the first line.

20 cm 2 ... 1 dm 2

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

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

Rice. 5. Various sizes

Today in the lesson we got acquainted with another unit of area, a square decimeter, learned how to convert square decimeters into square centimeters and compare values.

This concludes our lesson.

Bibliography

M.I. Moro, M.A. Bantova and others. Mathematics: Textbook. Grade 3: in 2 parts, part 1. - M .: "Enlightenment", 2012.
M.I. Moro, M.A. Bantova and others. Mathematics: Textbook. Grade 3: in 2 parts, part 2. - M .: "Enlightenment", 2012.
M.I. Moreau. Mathematics lessons: Guidelines for teachers. Grade 3 - M.: Education, 2012.
Regulatory document. Monitoring and evaluation of learning outcomes. - M.: "Enlightenment", 2011.
"School of Russia": Programs for elementary school. - M.: "Enlightenment", 2011.
S.I. Volkov. Mathematics: Testing work. Grade 3 - M.: Education, 2012.
V.N. Rudnitskaya. Tests. - M.: "Exam", 2012.

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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 \u003d ... cm 2

4 dm 2 \u003d ... cm 2

6 dm 2 = ... cm 2

8 dm 2 = ... cm 2

9 dm 2 = ... cm 2

3. Express these quantities 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. Make a task for your comrades on the topic of the lesson.

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

Initial value

Converted value

More about the square

General information

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

Ar

Hectare

Acre

barn

Area calculation

Area formulas

Square: square side.
Rectangle: product of the parties.
Triangle (side and height are known): the product of a side and the height (the distance from that 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 are the sides, and α is the angle between them.
Equilateral triangle: side, squared, divided by 4 times the square root of three.
Parallelogram: the product of a side and the height measured from that side to the opposite side.
Trapeze: the sum of two parallel sides multiplied by the height, divided by two. Height is measured between these two sides.
A circle: the product of the square of the radius and π.
Ellipse: product of semiaxes and π.

Surface area calculation

planimeter

Area properties theorem

Geographic features with the largest area

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