Tasks for finding the perimeter and area. Tasks for finding the perimeter and sides of geometric shapes material in mathematics (grade 2)

Lesson and presentation on the topic: "Perimeter and area of ​​a rectangle"

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What are rectangle and square

Rectangle Is a quadrilateral with all angles right. This means that the opposite sides are equal to each other.

Square Is a rectangle with equal sides and corners. It is called a regular quadrilateral.

Quadrilaterals, including rectangles and squares, are denoted by 4 letters - vertices. To designate the vertices, Latin letters are used: A, B, C, D...

Example.

It reads like this: quadrilateral ABCD; square EFGH.

What is the perimeter of a rectangle? Perimeter calculation formula

Perimeter of a rectangle Is the sum of the lengths of all sides of the rectangle or the sum of the length and width times 2.

The perimeter is denoted by a Latin letter P... Since the perimeter is the length of all sides of the rectangle, the perimeter is written in units of length: mm, cm, m, dm, km.

For example, the perimeter of the rectangle ABCD is denoted as P ABCD, where A, B, C, D are the vertices of the rectangle.

Let's write the formula for the perimeter of the quadrangle ABCD:

P ABCD = AB + BC + CD + AD = 2 * AB + 2 * BC = 2 * (AB + BC)

Example.
A rectangle ABCD with sides is given: AB = СD = 5 cm and AD = BC = 3 cm.
Let us define P ABCD.

Solution:
1. Let's draw a rectangle ABCD with the original data.
2. Let's write a formula for calculating the perimeter of a given rectangle:

P ABCD = 2 * (AB + BC)

P ABCD = 2 * (5cm + 3cm) = 2 * 8cm = 16cm

Answer: P ABCD = 16 cm.

Formula for calculating the perimeter of a square

We have a formula for determining the perimeter of a rectangle.

P ABCD = 2 * (AB + BC)

Let's use it to define the perimeter of the square. Considering that all sides of the square are equal, we get:

P ABCD = 4 * AB

Example.
A square ABCD with a side equal to 6 cm is given. Let us determine the perimeter of the square.

Solution.
1. Let's draw a square ABCD with the original data.

2. Recall the formula for calculating the perimeter of a square:

P ABCD = 4 * AB

3. Let's substitute our data into the formula:

P ABCD = 4 * 6cm = 24cm

Answer: P ABCD = 24 cm.

Tasks for finding the perimeter of a rectangle

1. Measure the width and length of the rectangles. Determine their perimeter.

2. Draw a rectangle ABCD with sides 4 cm and 6 cm. Determine the perimeter of the rectangle.

3. Draw a square СEOM with a side of 5 cm. Determine the perimeter of the square.

Where is the calculation of the perimeter of a rectangle used?

1. Given a piece of land, it needs to be surrounded by a fence. How long will the fence be?

In this task, it is necessary to accurately calculate the perimeter of the site so as not to buy extra material for building a fence.

2. The parents decided to make repairs in the children's room. You need to know the perimeter of the room and its area in order to correctly calculate the number of wallpapers.
Determine the length and width of the room you live in. Determine the perimeter of your room.

What is the area of ​​a rectangle?

Square Is a numerical characteristic of a figure. The area is measured in square units of length: cm 2, m 2, dm 2, etc. (centimeter squared, meter squared, decimeter squared, etc.)
In calculations it is denoted by a Latin letter S.

To determine the area of ​​a rectangle, multiply the length of the rectangle by its width.
The area of ​​the rectangle is calculated by multiplying the length of the AK by the width of the CM. Let's write it down as a formula.

S AKMO = AK * KM

Example.
What is the area of ​​an AKMO rectangle if its sides are 7 cm and 2 cm?

S AKMO = AK * KM = 7 cm * 2 cm = 14 cm 2.

Answer: 14 cm 2.

Formula for calculating the area of ​​a square

The area of ​​a square can be determined by multiplying the side by itself.

Example.
V this example the area of ​​the square is calculated by multiplying side AB by the width of BC, but since they are equal, it multiplies side AB by AB.

S ABCO = AB * BC = AB * AB

Example.
Determine the area of ​​an AKMO square with a side of 8 cm.

S AKMO = AK * KM = 8 cm * 8 cm = 64 cm 2

Answer: 64 cm 2.

Tasks for finding the area of ​​a rectangle and square

1. A rectangle with sides of 20 mm and 60 mm is given. Calculate its area. Write your answer in square centimeters.

2. A summer cottage plot measuring 20 m by 30 m was purchased. Determine the area of ​​the summer cottage, write down the answer in square centimeters.

Before solving the problem of finding the perimeter and area geometric shapes, let me remind you that….

Level I

1.The length of the rectangle is 8 dm, the width is 7 dm. Find his area.

2. The side length of the square is 6 cm. Find out the area and perimeter of the square.

3. The rectangle has a length of 7 cm, a width of 5 cm. Find out the area and perimeter of the rectangle.

4. Find the perimeter and area of ​​the 6cm and 8cm rectangle.

5. The length of the rectangle is 8 dm, the width is 5 dm. Find his area.

6.Calculated the area of ​​a rectangle whose side lengths are 6 mm and 8 mm.

7.The width of the rectangle is 7 inches and the length is 12 inches. Calculate the area.

8. The length of the rectangle is 9 dm, the width is 7 cm. Find its area.

9. The length of the side of the square is 6 cm. Find out the area.

10.Calculated the perimeter of a square with a side of 4 cm.

11. The width of the rectangle is 9 inches and the length is 6 inches longer. Find its area.

12. The length of the rectangle is 5 dm, the width is 4 cm less. Find the P and S of this rectangle.

13. Draw a rectangle, the length of one side of which is 2 cm, and the length of the other is 3 times longer. Find its perimeter and area.

14. Draw a rectangle, the length of one side of which is 6 cm, and the length of the other is 2 times longer. Find its perimeter and area.

15. Draw a rectangle that is 2 cm wide and 3 cm longer. Calculate its perimeter.

16. The side of the square is 3 cm. What is the perimeter?

17. The sheet of paper is square. Its side is 10 cm. What is the perimeter?

18. Draw a 6 cm square. Find its perimeter. The perimeter of a square is 28 cm. What is its side?

19. The width of the rectangular window is 4 dm, and the length is 2 times longer. Calculate the area of ​​the window.

20. The width of the rectangle is 4 dm, and the length is 5 times the width. Find the area of ​​the rectangle.

21. The area of ​​the rectangle is 36 cm², its length is 9 cm. What is the width of the rectangle?

II level

1. Draw a rectangle, the length of one side of which is 2 cm, and the length of the other is 4 times longer. Find its perimeter and area.

2. The length of the rectangle is 5 dm, the width is 4 cm less. Find the P and S of this rectangle.

3. Given: rectangle, a = 8 dm, b - 2 cm less. Find P and S.

4.The length of the rectangle is 12 cm and its width is 2 cm less. Find the area and perimeter of the rectangle.

5. The sum of the two sides of the square is 12 dm. Find the perimeter and area of ​​the square.

6. Find the length of the rectangle by its width - 8 inches and perimeter –30 inches.

7.The perimeter of a square is 32 cm. What is its side?

8. The perimeter of the triangle is 21 cm. Put on the length of the third side of this triangle if the lengths of the two sides are 7 cm and 8 cm.

9. The perimeter of the rectangle is 20 cm. The length of its side is 6 cm. Find out the width of the rectangle and draw it.

10. The area of ​​the rectangle is 270 cm2, its length is 9 dm. Find the perimeter of this rectangle.

11.Perimeter rectangle is 54 m. Find the area of ​​this rectangle if one side of it is 18 m.

12. Find the area of ​​a square whose perimeter is 360 mm.

13. The perimeter of the rectangle is 40 cm. One side is 5 cm. What is its area?

14. Draw a square whose perimeter is equal to the perimeter of a rectangle with sides of 2 cm and 6 cm.

15. A rectangular suburban area has a length of 20 m and a width of 12 m. How long should the fence be placed around the area?

16. The perimeter of a square is equal to the perimeter of a triangle with sides of 6 cm, 3 cm and 7 cm. What is the length of a side of the square?

17. Which figure has a larger area and by how much: a square with a side of 4 cm or a rectangle with sides of 2 cm and 6 cm?

18. The perimeter of the rectangle is 54 m. Find the area of ​​this rectangle if one of its sides is 18 m.

19. The perimeter of the square sandbox is 12 m. Find the area of ​​this sandbox.

20. Write everything possible options the length and width of the rectangle if its perimeter is 24 cm.

Compiled by Kislova Lyudmila Borisovna

Sections: Primary School

Lesson construction:

1. Organization and motivation of students for activities in the lesson.
2. Organization of perception of new material based on visual material
3. Organization of comprehension.
4. Initial check of understanding of new material.
5. Organization of primary consolidation and independent analysis of educational information.
6. Application of the knowledge gained at the workshop.

Lesson objectives:

1. Educational. Ensure the assimilation by students of finding the area and perimeter of geometric shapes;

visual perception of the material in the lesson; it is meaningful to understand what area and perimeter are.

2. Developing. Use developmental exercises in the lesson, activate

mental activity of schoolchildren.

3. Educational. To ensure the development of the value-semantic culture of students;

motivation for the ability to correctly achieve the set goal -

coincidence of expectation and result.

Equipment:

1. MI Moro et al. "Mathematics" - a textbook for grade 3 primary school, 1 part.
2. Workbook mathematics.
3. Pen, ruler, pencil, triangle, scissors.
4. Models of geometric shapes for finding the area.
5. Above the board are posters with formulas for finding the area and perimeter.

Means of education:

1. Didactic material.
2. Visual aids.

Training methods:

1. Comparison of items.
2. Comparisons of ways to find the area of ​​the same figure.

During the classes.

1. Organizing time and message of the topic of the lesson.

Teacher: Hello guys. Today we will continue our study of a large topic called “Area and Perimeter”. The topic of our lesson today: "The ability to apply knowledge in finding the perimeter and area of ​​a complex figure." A complex shape is a geometric shape made up of several simpler shapes. First, we will repeat what we have learned in previous lessons.

II. Verbal counting.

Development tasks.

Teacher: Find the area of ​​this figure if the side of the square is 1 cm.

The figure is depicted on the board.

Pupil: If 1 square has an area of ​​1 cm 2, and there are 5 squares, then the area of ​​this figure is 5 cm 2.

Teacher: Right. Next task. Remove 3 sticks to leave 3 of these squares.

The student goes to the board and removes 3 sticks.

Teacher: Remove 4 sticks to leave 3 of the same squares.

The student goes to the board and removes 4 sticks. Solution.

III. Work on the topic of the lesson

Teacher: What geometric shapes do you already know?

Disciple: Rectangle.

Disciple: Square.

Teacher: Right. What do we know about the square?

Student: A square has 4 sides and 4 corners.

Teacher: Right. What property do the sides of a square have?

Disciple: They are equal.

Teacher: Right. And what are the corners of the square?

Disciple: They are straight.

Teacher: With what can we build a right angle?

Disciple: With the help of a triangle.

Teacher: Let's build a 4 cm square in your notebook. What tools will we use to draw a square?

Student: With a ruler, pencil and triangle.

Pupils build a square in their notebooks and paint it.

Teacher: This geometric figure. How do I find the perimeter and area of ​​this square?

Disciple: The perimeter is the sum of all its sides. Sides at square 4. So, add 4 4 times.

Teacher: How to write this down?

Pupils make a note in a notebook: “ Find the area of ​​the figure F1 ”.

The student is called to the blackboard, and he writes: P = 4 + 4 + 4 + 4 = 16 (cm)

Pupils write in a notebook.

Teacher: In what units is the perimeter still measured?

Disciple: In centimeters, in millimeters, in meters, in decimeters, in kilometers.

Teacher: Well done! How else can you record the perimeter?

Disciple: By multiplication.

The student writes on the board: P = 4 4 = 16 (cm)

Pupils write in notebooks.

Teacher: What is the area of ​​a square?

Student: We multiply the length of the square by its width. Since the sides of the square are equal, then

S = 4 4 = 16 (cm 2)

Pupils write in a notebook and write down - “ Answer: S = 16 cm 2 ”.

Teacher: What other units of measure of area do you know?

Pupil: square centimeter, square decimeter, square meter, square millimeter.

Teacher: Now let's complicate the task. There is a card in front of you.

This card shows a square the same as in your notebook. In the middle of this square is another 2 cm square. Now you take your scissors and carefully cut this small square.

Students do this work and write in a notebook: “ Find the area of ​​the figure F2 ”.

Teacher: We have a figure "with a window" - F2. How can you find the area of ​​this interesting figure? The area of ​​the square is already known and is equal to 16 cm 2.

Disciple: You need to find the area of ​​a small square with a side of 2 cm.

The student goes to the blackboard and writes down - S2 = 2 2 = 4 (cm 2)

Students write in a notebook

Disciple: Subtract the area of ​​the small one from the area of ​​the large square.

Teacher: Right.

The student writes on the board - S = S1 - S2 = 16 - 4 = 12 (cm 2)

Pupils write in a notebook.

Teacher: Take a close look at this figure and tell me how else you can measure the area? Can this figure be cut somehow to get the figures you already know?

Students think and say different options.

One of the options turned out to be very interesting.

Student: You can cut it so that you get rectangles and shows on the board how this can be done.

Pupils cut the shape as shown on the board.

Teacher: What is the area of ​​a rectangle?

Disciple: You need to multiply the length by the width.

Teacher: You have four shapes. What can you say about them?

Disciple: Two figures, like twins, are the same, and the second two are also the same.

You can find the area of ​​one shape and multiply by 2.

The student decides on the blackboard: S1 = 1 4 = 4 (cm 2)

S2 = 1 2 = 2 (cm 2)

S = 2 S1 + 2 S2 = 2 4 + 2 2 = 8 + 4 = 12 (cm 2)

Teacher: Well done! We got the same area value as before.

Pupils write in a notebook - “ Answer: S = 12 cm 2. "

Teacher: You are probably tired?

It's time to rest.

I offer fatigue

Take physical education off.

IV. Physical education.

Every day in the morning
Doing exercises (walking on the spot).
We really like to do in order:
Have fun walking (walking)
Raise your hands (hands up)
Squat and stand up (squat 4-6 times),
Jump and jump (10 jumps).

Teacher: And now they sat down at their desks and

take a look at the following model. Figure F3

How do you find the area of ​​this interesting figure?

Disciple: A triangle that stands out

can be cut off and inserted into the part where

the triangle "goes" inward.

Teacher: Let's take the scissors, cut off the triangle and substitute in the upper part.

What kind of figure did we get?

Disciple: Rectangle!

Teacher: How to find the area of ​​this rectangle,

If the parties are unknown to us.

Disciple: We can take a ruler and measure

the length and width of the rectangle.

Pupils make a note - “ Find the area of ​​the figure F3 ”.

Students measure the length and width with a ruler. It turns out the length, a = 6 cm, width b = 2 cm.

Student: The area of ​​this figure is S = 6 2 = 12 (cm 2).

Pupils write in a notebook and write down - “ Answer: S = 12 cm 2.

Teacher: But that's not all. Here is the next figure. It is necessary to find its area.

What is the figure in front of you?

Student: Triangle. But the area of ​​the triangle

we do not know how to find!

Teacher: It's true. From this triangle

let's make a rectangle. I'll give you a hint. Figure F4

First, we fold this triangle in half.

Pupils: We get it! Right

turn over the side.

You will get a rectangle.

Disciple: We measure with a ruler

length a and width b, and by S = a

we find the area.

Teacher: If we are when measuring, we

we get that the length

will be expressed in mm and width in cm,

what should we do?

Pupil: Be sure to translate the length and width into one unit of measurement.

Pupils write in a notebook: “ Find the area of ​​the figure F4 ”.

V. Work in pairs.

Teacher: And now I propose to work in pairs. There are two of you at your desk. One student (option I) finds the perimeter of this figure, and the second (option II) finds the area.

To do this, draw this figure in a notebook. After you complete the task, exchange notebooks and check the results with each other.

Students complete assignment and results

write down in a notebook.

Teacher: What did you do?

Student: A square with a side of 3 cm. P = 3 4 = 12 (cm)

S = 3 3 = 9 (cm 2) 3 cm

Students write: “ Answer: P = 12 cm, S = 9 cm 2.

Teacher: Well done! And now I suggest you work on your own.

Find the area of ​​the next shape. She lies in front of you.

Vi. Independent work to consolidate the studied material.

The teacher distributes pre-prepared figures.

Students on their own, without the help of a teacher, cut this figure, get three rectangles.

The disciples record: “ Find the area of ​​the figure F5 ”.

Students find S1 = 4 3 = 12 (cm 2), S2 = 2 1 = 2 (cm 2), then find the area of ​​this figure: S = S1 + S2 + S2 = 12 + 2 + 2 = 16 (cm 2 ) and write in a notebook, then

write: “ Answer: S = 16 cm 2 ”.

Teacher: Did you like the lesson?

Pupils: Yes.

Teacher: What did you learn new in this lesson?

Disciple: We have learned to find the area and perimeter of complex shapes. It turned out to be very simple. We need to think a little and rebuild or remake this figure into the perimeter and area that we already know how to find.

Teacher: I am very glad that you liked it. At home, repeat the formulas for finding the perimeter and area of ​​a square and rectangle once again; remember how to translate one unit

to another. The following students answered well today. ... ...

The teacher gives marks.

Vii. Homework: textbook p. 77 No. 8.

CLASS 3

1) The side of the square is 3 cm. What is the perimeter?

2) The length of the rectangle is 5 cm and the width is 4 cm. What is the perimeter?

3) The table top is rectangular. The length is 90 cm and the width is 60 cm. What is the perimeter?

4) Draw a 6 cm square. Find its perimeter.

5) The sheet of paper is square. Its side is 10 cm. What is the perimeter?

6) A rectangular vegetable garden has a border of 1000 m. What dimensions can the length and width of the vegetable garden have? (Give several solutions in whole numbers.)

7) The side of the rectangle is a = 4 cm, and b is 2 cm longer. What is the perimeter?

8) The side of the square is 6 cm. What is the perimeter?

9) Draw a rectangle 4 cm wide and twice as long. Find its perimeter.

10) The side of the rectangle is a = 4 cm, and the perimeter is 14 cm. What is the side b?

11) The perimeter of a square is 24 cm. What is its side?

12) One side of the rectangle is 1 dm, this is 3 cm larger than the other side. Find out the perimeter and draw a rectangle.

13) The side of the rectangle is a = 7 cm, and b is 2 cm shorter. What is the perimeter of the rectangle?

14) The side of the rectangle is a = 5 cm, P = 16 cm. What is the side b?

15) The perimeter of the rectangle is 20 cm. The length of its side is 6 cm. Find out the width of the rectangle and draw it.

16) Write down all the possible lengths and widths of the rectangle if its perimeter is 24 cm.

17) The perimeter of the square is 28cm. What is his side equal to?

18) The plot of land has the shape of a rectangle, the length of which is 69 m and the width is 31 m. How long is the fence surrounding this plot?

19) Draw a 5 cm square. Find its perimeter.

20) What is the side of the chalkboard if its perimeter is 10 m and the width is 20 dm?

21) The perimeter of the rectangle is 64 cm.Find its length if the width is 14 cm.

22) What is the perimeter of a triangle with sides of 10 cm, 18 cm and 9 cm?

23) In a rectangular park, 160 m long and 80 m wide, an alley was made at a distance of 2 m from the fence. Find its length.

24) Find out the perimeter of the hockey rink if it is 15 m long and 90 dm wide.

25) The plot of land has the shape of a rectangle, the width of which is 28 m, and the length is 14 m longer. It is surrounded by wire in 7 rows. How many meters of wire did it take?

26) How much tape should I buy for covering a carpet 2 m long and 15 dm wide?

27) The length and width of 1 sheet of roofing steel together is 2130 mm. What is the length and width of the sheet if the length is twice the width?

28) Write down all possible lengths and widths of a rectangle if its perimeter is 36 cm (in whole numbers).

29) Draw a rectangle 6 cm long and half the width. What is its perimeter?

30) Which piece of land has a large fence: square with a side of 40 m or rectangular with sides of 40 m and 30 m?

31) The sum of the sides of a triangle with three equal sides 27 dm. What is his side equal to?

32) Find the perimeter of a rectangle 5 inches long and 7 cm wide.

33) Write down all possible lengths and widths of the rectangle if its perimeter is 48 cm (in whole numbers).

34) The room is 8 m long and 4 m wide. How many pieces of border do you need for pasting a room? The length of the curb piece is 12 m.

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