Problems on finding perimeter and area. Problems to find the area and perimeter of geometric shapes What is the area of a rectangle

Sections: Primary school

Lesson structure:

Organization and motivation of students for activities in the lesson.
Organization of perception of new material based on visual material
Organization of comprehension.
Initial check of understanding of new material.
Organization of primary consolidation and independent analysis of educational information.
Application of acquired knowledge at the workshop.

Lesson objectives:

Educational. Ensure that students learn to find the area and perimeter of geometric figures;

visual perception of material in the lesson; It makes sense to understand what area and perimeter are.

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

mental activity of schoolchildren.

3. Educational. Ensure the development of students’ value-semantic culture;

motivation for the ability to correctly achieve the goal -

coincidence of expectation and result.

Equipment:

M.I.Moro and others. “Mathematics” - textbook for grade 3 primary school, part 1.
Workbook in mathematics.
Pen, ruler, pencil, triangle, scissors.
Models of geometric figures for finding area.
Above the board are posters with formulas for finding area and perimeter.

Learning Tools:

Didactic material.
Visual aids.

Teaching methods:

Comparison of objects.
Comparison of methods for finding the area of the same figure.

Progress of the lesson.

1. Organizational moment and a message about the topic of the lesson.

Teacher: Hello, guys. Today we will continue to study 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 figure is a geometric figure consisting of several simple figures. First, let's repeat what we learned in previous lessons.

II. Oral 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.

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

Teacher: Correct. Next task. Remove 3 sticks to leave 3 such squares.

The student goes to the board and removes 3 sticks.

Teacher: Remove 4 sticks so that 3 of the same squares remain.

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?

Student: Rectangle.

Student: Square.

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

Student: A square has 4 sides and 4 corners.

Teacher: Correct. What properties do the sides of a square have?

Student: They are equal.

Teacher: Correct. What are the angles of a square?

Student: They are straight.

Teacher: What can we use to construct a right angle?

Student: Using a triangle.

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

Student: Using a ruler, pencil and triangle.

Students use their notebooks to build a square and color it.

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

Student: The perimeter is the sum of all its sides. A square has 4 sides. This means we add 4 4 times.

Teacher: How to write this down?

Students write in their notebooks: “ Find the area of figure F1”.

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

Students write in their notebooks.

Teacher: In what other units is perimeter measured?

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

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

Student: Using multiplication.

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

Students write in their notebooks.

Teacher: What is the area of the square?

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

S = 4 4 = 16 (cm 2)

Students make a note in their notebook and write down - “ Answer: S = 16 cm 2”.

Teacher: What other units of area do you know?

Student: 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 the one in your notebook. In the middle of this square is another square with a side of 2 cm. Now you will take scissors and carefully cut out this small square.

Students do this work and write in their notebook: “ Find the area of 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.

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

The student goes to the board and writes down – S2 = 2 2 = 4 (cm 2)

Students write in their notebooks

Student: Subtract the area of the small square from the area of the large square.

Teacher: Correct.

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

Students make notes in their notebooks.

Teacher: Look carefully at this figure and tell me how else you can measure the area? Is it possible to somehow cut this figure to get shapes that are already familiar to you?

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.

Students cut the shape as shown on the board.

Teacher: What is the area of a rectangle?

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

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

Student: Two figures are like twins - identical, and the second two are also identical.

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

The student solves on the board: 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.

Students write in their notebooks: “ Answer: S = 12 cm 2.”

Teacher: Are you probably tired?

It's time to rest.

I suggest fatigue

Take off for a physical education minute.

IV. Physical education minute.

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

Teacher: And now we sat down at our desks and

look at the next model. Figure F3

How to find the area of this interesting figure?

Student: A triangle that protrudes

can be cut off and placed in the part where

the triangle “goes” inward.

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

What kind of figure have we got?

Student: Rectangle!

Teacher: How to find the area of this rectangle,

If the parties are unknown to us.

Student: We can take a ruler and measure

length and width of the rectangle.

Students make a note: “ Find the area of figure F3”.

Students use a ruler to measure the length and width. The result is length a = 6 cm, width b = 2 cm.

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

Students make a note in their notebook and write down: “ Answer: S = 12 cm 2.

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

What kind of figure is in front of you?

Student: Triangle. But the area of the triangle

We don't know how to find!

Teacher: That'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

Students: We understand! Right

turn the side over.

You will get a rectangle.

Student: Using a ruler we measure

length a and width b, and by S = a · b,

find the area.

Teacher: If we are measuring, we

we find that the length

will be expressed in mm and the width in cm,

what should we do?

Student: Be sure to convert the length and width into one unit of measurement.

Students write in their notebooks: “ Find the area of figure F4”.

V. Work in pairs.

Teacher: Now I suggest working in pairs. There are two of you at your desk. One student (option I) finds the perimeter of a given figure, and the second (option II) finds the area.

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

Students complete the task and results

write down in a notebook.

Teacher: What did you do?

Student: Square with side 3 cm. P = 3 4 = 12 (cm)

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

Students write down: “ 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 figure. She lies in front of you.

VI. Independent work to consolidate the studied material.

The teacher distributes pre-prepared figures.

Students independently, without the help of a teacher, cut this figure and get three rectangles.

Students make a note: “ 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 make a note in the notebook, then

write down: “ Answer: S = 16 cm 2”.

Teacher: Did you like the lesson?

Students: Yes.

Teacher: What new did you learn in this lesson?

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

Teacher: I'm very glad that you liked it. At home, repeat the formulas for finding the perimeter and area of a square and rectangle; remember how to convert one unit

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

The teacher gives grades.

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

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

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Trainer for 3rd grade "Rules and exercises in mathematics"
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What are rectangle and square

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

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

Quadrangles, including rectangles and squares, are designated by 4 letters - vertices. Latin letters are used to designate vertices: A, B, C, D...

Example.

It reads like this: quadrilateral ABCD; square EFGH.

What is the perimeter of a rectangle? Formula for calculating perimeter

Perimeter of a rectangle is the sum of the lengths of all sides of the rectangle or the sum of the length and width multiplied by 2.

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

Let's write down the formula for the perimeter of a quadrilateral ABCD:

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

Example.
Given a rectangle ABCD with sides: AB=CD=5 cm and AD=BC=3 cm.
Let's define P ABCD.

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

P ABCD = 2 * (AB + BC)

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

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 determine the perimeter of a square. Considering that all sides of the square are equal, we get:

P ABCD = 4 * AB

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

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

2. Let us 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 * 6 cm = 24 cm

Answer: P ABCD = 24 cm.

Problems to find 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 SEOM with a side of 5 cm. Determine the perimeter of the square.

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

1. A plot of land has been given; 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 excess material for building a fence.

2. Parents decided to renovate the children's room. You need to know the perimeter of the room and its area in order to correctly calculate the amount of wallpaper.
Determine the length and width of the room in which you live. Determine the perimeter of your room.

What is the area of a rectangle?

Square- This numerical characteristic figures. 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 AC by the width of the CM. Let's write this down as a formula.

S AKMO = AK * KM

Example.
What is the area of rectangle AKMO 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.
In this example, the area of a square is calculated by multiplying the side AB by the width BC, but since they are equal, the result is multiplying the side AB by AB.

S ABCO = AB * BC = AB * AB

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

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

Answer: 64 cm 2.

Problems to find the area of a rectangle and square

1. Given a rectangle with sides 20 mm and 60 mm. Calculate its area. Write your answer in square centimeters.

2. A dacha plot measuring 20 m by 30 m was purchased. Determine the area of the dacha plot and write the answer in square centimeters.

Problems on finding area and perimeter

geometric shapes

Compiled by:

teacher primary classes

MKOU Secondary School No. 1 named after A.M. Gorky

urban district city of Frolovo

Kislova Lyudmila Borisovna

Frolovo – 2014

I level.

1. The length of the rectangle is 8 dm, width is 7 dm. Find its area.2.The length of the side of the square is 6 cm. Find out the area and perimeter of the square.3. A rectangle has a length of 7 cm and a width of 5 cm. Find out the area and perimeter of the rectangle.4.Find the perimeter and area of a rectangle with sides 6 cm and 8 cm.

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

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

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

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

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

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

11. The width of the rectangle is 9 dm, and the length is 6 dm more. 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 greater. 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 greater. Find its perimeter and area.

15.Draw a rectangle whose width is 2 cm and whose length is 3 cm more. Calculate its perimeter.

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

17. A sheet of paper has a square shape. Its side is 10 cm. What is the perimeter?

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

19. The width of a rectangular window is 4 dm, and the length is 2 times greater. 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 greater. 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: a rectangle, a = 8 dm, c - 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 based on its width - 8 dm and perimeter - 30 dm.

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

8. The perimeter of the triangle is 21 cm. Find 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 sq. cm, its length is 9 dm. Find the perimeter of this rectangle.

11. The perimeter of the rectangle is 54 m . Find the area of this rectangle if one side 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 2 cm and 6 cm.

15. A rectangular dacha plot is 20 m long and 12 m wide. How long should a fence be placed around the plot?

16. The perimeter of a square is equal to the perimeter of a triangle with sides 6 cm, 3 cm and 7 cm. What is the length of the 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 side is 18 m.19. The perimeter of a square sandbox is 12 m. Find the area of this sandbox.20.Write all possible lengths and widths of the rectangle if its perimeter is 24 cm.

Internet resources used

Problems on finding perimeter and area. Simple tasks + test. Difficult tasks + test. Memo and test for it

"Test"

1. The length of the rectangle is 8 cm and the width is 5 cm shorter. What is its perimeter?

2. How much greater is the perimeter of a square with a side of 1 dm 2 cm than the perimeter of a square with a side of 5 cm?

3. One side of the triangle is 13 cm, the second is 9 cm more than the first, and the third is 4 cm less than the first. Find the perimeter of triangle ABC.

4. How much less is the area of a rectangle with sides 3 cm and 4 cm than the area of a rectangle with sides 4 cm and 5 cm?

5. How much greater is the area of a square with a side of 5 cm than the area of a square with a side of 3 cm?