What is a perimeter? What is a perimeter and its application in practice Rule what is a perimeter

We do not use many formulas from the school mathematics course in everyday life. However, there are equations that are used, if not on a regular basis, then from time to time. One of these formulas is the calculation of the perimeter of a figure.

What is a perimeter?

The perimeter is the total length of all sides of a geometric figure. For its designation, the letter of the Latin alphabet "R" is used. Simply put, to find the perimeter, you need to measure the lengths of all sides of a geometric figure and add the resulting values. The length is calculated with a conventional measuring instrument, such as a ruler, tape measure, centimeter tape, and so on.

The units of measurement are respectively centimeters, meters, millimeters and other measures of length. The length of a side of a polygon is calculated by applying a measuring device from one vertex to another. The beginning of the division scale of the device must coincide with one of the vertices. The second numeric value that the other vertex hits is the length of the side of the polygon. In the same way, it is necessary to measure all the lengths of the sides of the figure and add the resulting values. The unit of perimeter is the same unit used to measure the side of a shape.

A rectangle should be called a geometric figure, which consists of four sides of different lengths and three corners of which are straight. When constructing such a figure on a plane, it turns out that its sides will be equal in pairs, but not all are equal to each other. What is the perimeter of a rectangle? It is also the total length of all figure lengths. But since two sides of a rectangle have the same value, in calculating the perimeter, you can add the lengths of two adjacent sides twice. The unit of measurement for the perimeter of a rectangle is also the generally accepted units of measurement.

A triangle should be called a geometric figure that has three angles (both of different values ​​and the same) and consists of segments formed from the points of intersection of the rays that form the angles. A triangle has three sides and three angles. Two of the three sides can be equal in it. Such a triangle should be considered isosceles. There are such figures in which all three sides are equal to each other. It is customary to call such triangles equilateral.

What is the perimeter of a triangle? Its calculation can be carried out by analogy with the perimeter of a quadrilateral. The perimeter of a triangle is equal to the total length of the lengths of its sides. Calculating the perimeter of a triangle in which two sides are equal - isosceles - is simplified by multiplying one length of equal sides by two. To the value obtained, you must add the value of the length of the third side. Calculating the perimeter of a triangle with equal sides can be reduced to a simple calculation of the product of one length of a side of a triangle by three.

Applied Perimeter Value

The calculation of the perimeter in everyday life is used in many areas, but most often when performing construction, geodesic, topographic, architectural, planning work. But the listed scope of perimeter calculation, of course, is not limited.

For example, when performing geodetic and topographic works, it is very often necessary to calculate the perimeter of the boundaries of a certain area. But in practice, the plots rarely have the correct shape. Therefore, the calculation of the length of the perimeter occurs according to the formula for calculating the sum of the lengths of all sides of the section.

The need to calculate the perimeter of the site is very often due to the fact that you need to know how much material is required to install fences. Even a simple personal plot needs to measure the perimeter in order to competently enclose it with a fence.

Measuring devices on the ground

To calculate the perimeter on the ground, it is impossible to use a simple student ruler. Therefore, specialists use special devices. Of course, the simplest and most affordable option is to measure the length of the site boundary in steps. The step size of an adult is approximately one meter. Sometimes one meter and twenty centimeters. But this method is very inaccurate and gives a large measurement error. It is suitable if there is no need to accurately calculate the length of the border, but there is a need to simply estimate the approximate length.

For a more accurate calculation of the length of the sides of the site and, accordingly, the perimeter, there are special devices. First of all, you can use a special metal tape measure or a regular wire.

There are also special measuring devices such as rangefinders. Devices are optical, laser, light, ultrasonic. It should be remembered that the farther the rangefinder is able to measure the distance, the higher its error. Such devices are used in geodetic and topographic surveys.

Development of an extracurricular lesson in arithmetic in grade 2 on the topic: The perimeter of a triangle and a square

Extracurricular lesson in arithmetic Grade 2.

How to find the perimeter of a rectangle.

Topic: Perimeter of triangle and square.

1. Introduce the concept of the perimeter of a triangle and a square. 2. Learn to use formulas in practice triangle and square. 3. Development of logical thinking, speech.

Equipment: visualization Triangle, cut triangles, 12 fragments of figures, 2 triangles, perimeter formulas.

Literature: In the country of interesting figures, Geometric construction 2 cells.

II. Attention exercise.

Look closely at the shapes and remember how the dots are placed.

For now, I will close the board, and you remember, try to draw the layout on your own pieces of paper.

Let's check. Raise your hand who hasn't made a single mistake. Well done! Who made mistakes, be careful.

III. Research of new material.

And now we will go to the delightful country of Geometry. And to whom to visit, you have to guess. Listen to the poem Triangle and Square.

Once upon a time there were two brothers: a Triangle with a Square. Senior - Square, friendly, pleasant. Junior - triangular - Eternally dissatisfied. He began to ask Kvadrat: Why are you angry, brother? He yells to him: -Look: You are fuller than me and more extensive. I have only three corners, you have four of them! But the square replied: -Brother! I'm older, I'm a Square! I, - said even more tenderly: - It is not known who is more needed! But the night set in, and to the brother; Bumping on the tables, The younger climbs furtively, Cut corners for the older. Leaving, he said: - I wish you pleasant dreams! I went to bed - I was square, And you wake up without corners. But the next morning, the younger brother of the Terrible Vengeance was not happy.

Guys, let's see why the younger brother of the terrible revenge was not happy. Who will go to the board and cut the corners of the square?

He looked - no Square Numb ... stood without words ... Is that revenge? Now my brother has Eight new corners!

What happened to the square?

So where are we going on our trip?

That's right, the city of triangles and squares. And the Triangle will accompany us. But she will accompany us in this case, if we answer questions.

1. What is the difference between a triangle and a square?

2. What is remarkable about the square?

Well done! You can set off on a trip.

So we arrived in the city of Triangles and Squares and a new task awaits us.

Task 1: Can you see?

How many triangles are hidden in this house? (5) What about quadrilaterals? (1)

Task 2: There are 9 triangles in the drawing. Can you see them? Who will go and show?

Task 3: Look at the figure. How many quadrilaterals? (7) And how many squares are there? (3)

Practical task Who is faster

What is a perimeter triangle?

So what should we do to find the perimeter? (1. measure the length of the sides; 2. find their sum).

This is how the formula for the perimeter of triangles looks like: P \u003d a in c.

Using this formula, you can find the sum of the lengths of the sides of any triangle.

The sum of the lengths of the sides of a triangle is called...

Well done! Draw a square knowing only the length of one side and find the sum of the lengths of its sides. The side of the square is 4 cm. Can we draw a square knowing only one side? Why?

Guys, what do you think, what is the name of the sum of the lengths of the sides of a square?

That's right, the amount side lengths square is the perimeter. Let's derive a formula that can find the perimeter square with side a. Who will try?

Knowing that four times a means what can we do?

Yes, we can replace addition with multiplication, then we get the formula P = 4a. For a beautiful record, the number 4 is put in first place, and then the letter. In practice, this formula is used.

What have we been doing now?

What is a perimeter?

What is the formula for the perimeter of a triangle?

Read the formula for the perimeter of a square.

IV. Consolidation of the material covered.

1) Draw a square according to the given perimeters: in-1 - 8 cm, in-2 - 12 cm. 2) A triangle is given. Find its perimeter. 3) For the holiday, students decorate the outside of the school building from all quadrangular sides with flags. There are few flags, only 12. How to arrange them 4, 5, 6 on each side.

How to find the amount side lengths triangle and square?

Write down the formulas for the perimeter of a square and a triangle?

What is interesting about the square?

The triangle says goodbye and hopes to meet you again.

Development of an extracurricular lesson in mathematics in grade 2 on the topic: The perimeter of a triangle and a square

Abstracts

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The perimeter is the sum of the lengths of all sides, such as a rectangle, square. To find it, you need to add up all the sides. And if we have a square, then we need to multiply one side by 4.
For example.
rectangle:
width 5 cm
length 8 cm
5+5+8+8=26
square:
width and length 3 cm
3 times 4=12cm

The perimeter is the sum of the lengths of all sides of a geometric figure, denoted by the letter P, some formulas for finding the perimeter
triangle
P=a+b+c
rectangle
P=2*(a+b)
square
P=4*a

Related tasks:

1) find the sum of the angles of a convex dodecagon, each angle of a convex polygon = 135 * Find the number of sides of this polygon.

2) In a convex pentagon, 2 sides are equal, 3 side is 3 cm more, and 4 is 2 times more than 1 side, and 5 is 4 cm less than 4 cm. Find the sides of the pentagon if it is known that the perimeter = 34 cm

1) Two pumps working together fill the pool in 4 hours. The first pump fills the pool one and a half times faster than the second. How many hours does it take the first pump to fill the pool?

2) The perimeter of the parallelogram is 90 cm and the acute angle is 60°. The diagonal of a parallelogram divides its obtuse angle into parts in a ratio of 1:3. Find the length of the longest side of the parallelogram.

3) The second term of the arithmetic progression is 5, and its fourth term is 11. Find the sum of the first five terms of the progression.

4) The area of ​​the parallelogram is 〖24cm〗^2. The point of intersection of its diagonals is 2 cm and 3 cm away from the lines on which the sides lie. Find the perimeter of the parallelogram.

Content:

Calculating the perimeter of a rectangle is a fairly simple task. All you need to know is the width and length of the rectangle. If these values ​​are not given, you need to find them. This article will show you how.

Steps

1 Standard method

1. 1 Formula for calculating the perimeter. Basic formula for calculating the perimeter of a rectangle: P = 2 * (l+w).
   • Remember: the perimeter is the total length of all sides of the figure.
   • In this formula P- "perimeter" l- the length of the rectangle, w is the width of the rectangle.
   • Length always has a greater value than width.
   • Since the rectangle has two equal lengths and two equal widths, only one side is measured. l(length) and one side w(width) (even though the rectangle has four sides).
   • You can also write the formula as: P = l + l + w + w
2. 2 Find the length and width. In an ordinary mathematical problem, the length and width of a rectangle are usually given. If you are looking for the perimeter of a rectangle in real life, use a ruler or tape measure to find the length and width.
   • If you are calculating the perimeter of a rectangle in real life, use a tape measure or measuring tape to find the length and width of the desired area. If you are working outdoors, measure all sides to make sure the parallel sides do match.
   • For example: l= 14 cm, w= 8 cm
3. 3 Add the length and width. Plug the values ​​into the formula and add them up.
   • Note that, according to the order of operations, the mathematical expressions in parentheses are solved first.
   • For example: P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22)
4. 4 Multiply this amount by two (according to the formula).
   • Note that by multiplying the sum by two, you have taken into account the other two sides of the rectangle. By adding the width and length, you add only two sides of the figure. Since the other two sides of the rectangle are equal to two added together, the sum is simply multiplied by two to find the total sum of all four sides.
   • The resulting number will be the perimeter of the rectangle.
   • For example: P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22) = 44 cm
5. 5 Alternative method: fold l+l+w+w. Instead of adding two sides and multiplying them by two, you can simply add all four sides and find the perimeter of the rectangle.
   • If the concept of perimeter is difficult for you, then this method is just for you.
   • For example: P = l + l + w + w = ​​14 + 14 + 8 + 8 = 44 cm

2 Calculating the perimeter through the area and one side

1. 1 Formula for the area of ​​a rectangle. If you are given the area of ​​a rectangle, you must know the formula to calculate it to find the missing information to calculate the perimeter.
   • Remember: the area of ​​a figure is the value of the total space that is bounded by the sides of the figure.
   • Formula for calculating the area of ​​a rectangle: A=l*w
   • The formula for calculating the perimeter of a rectangle is: P=2*(l+w)
   • In the above formulas BUT- "square", P- "perimeter" l- the length of the rectangle, w is the width of the rectangle.
2. 2 Divide the area by the side given in the problem to find the other side.
   • Since you need to multiply the length by the width to calculate the area, dividing the area by the width gives you the length. Likewise, dividing the area by the length will give you the width.
   • For example: A= 112 cm2, l= 14 cm
     • A=l*w
     • 112 = 14*w
     • 112/14 = w
     • 8=w
3. 3 Add length and width. Now that you have the length and width values, you can plug them into the formula to calculate the perimeter of the rectangle.
   • The first step is to add the length and width, since this part of the equation is enclosed in brackets.
   • According to the order of evaluation, the action given in parentheses is performed first.
4. 4 Multiply the sum of the length and width by two. After you add the length and width of the rectangle, you can find the perimeter by multiplying the resulting number by two. This is necessary to add the remaining two sides of the rectangle.
   • The opposite sides of the rectangle are equal, which is why the sum of the length and width must be multiplied by two.
   • Both the length of the opposite sides and the width are the same.
   • For example: P \u003d 2 * (14 + 8) \u003d 2 * (22) \u003d 44 cm

3 Perimeter of a rectangular figure

1. 1 Write down the basic formula for determining the perimeter. Perimeter is the total length of all sides of a figure.
   • The rectangle has four sides. The sides that form the length are equal to each other and the sides that form the width are equal to each other. Thus, the perimeter is the sum of these four sides.
   • Rectangular figure. Consider an "L" shaped figure. Such a figure can be divided into two rectangles. However, when calculating the perimeter of a figure, such a division into two rectangles is not taken into account. The perimeter of the figure in question: , where S are the sides of the figure (see figure).
   • Each "s" is a separate side of the complex rectangle.
2. 2 In an ordinary mathematical problem, the sides of a figure are usually given. If you are looking for the perimeter of a rectangular shape in real life, use a ruler or tape measure to find its sides.
   • To explain, we introduce the following notation: L, W, l1, l2, w1, w2. uppercase L and W l and w
   • Thus the formula P = S1 + S2 + S3 + S4 + S5 + S6 is written as: (both formulas are essentially the same, but use different variables).
   • The variables "w" and "l" simply replace numbers.
   • Example: L = 14 cm, W = 10 cm, l1 = 5 cm, l2 = 9 cm, w1 = 4 cm, w2 = 6 cm.
     • note that l1+l2=L. Likewise, w 1+ w2=W.
3. 3 Fold the sides.
   • 48 cm

4 Perimeter of a rectangular figure (only some sides are known)

1. 1 Analyze the side values ​​given to you. You can find the perimeter of a rectangular figure if you are given at least one full length or full width and at least three partial widths and lengths.
   • For an "L"-shaped rectangular figure, the formula is used P = L + W + l1 + l2 + w1 + w2
   • In the above formula: P is the perimeter, uppercase L and W indicate the total length and width of the figure. Lowercase l and w indicate the incomplete length and width of the figure.
   • Example: L = 14 cm, l1 = 5 cm, w1 = 4 cm, w2 = 6 cm; Required to find: W, l2.
2. 2 Using the given side values, find the unknown sides. Please note that l1+l2=L. Likewise, w 1+ w2=W.
   • For example: L = l1 + l2; W = w1 + w2
     • L = l1 + l2
     • 14 = 5 + l2
     • 14 - 5 = l2
     • 9 = l2
     • W = w1 + w2
     • W=4+6
     • W=10
3. 3 Fold the sides. Substitute the values ​​in the formula and calculate the perimeter of the rectangular shape.
   • P = L + W + l1 + l2 + w1 + w2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 cm

What will you need

• Pencil
• Paper
• Calculator (optional)
• Ruler or tape measure (optional)

, broken line, etc.:

If you look closely at all these figures, you can select two of them, which are formed by closed lines (a circle and a triangle). These figures have a kind of border separating what is inside from what is outside. That is, the boundary divides the plane into two parts: the inner and outer area relative to the figure to which it belongs:

Perimeter

The perimeter is a closed boundary of a flat geometric figure that separates its inner area from the outer one.

Any closed geometric figure has a perimeter:

In the figure, the perimeters are marked with a red line. Note that the circumference of a circle is often referred to as the length.

The perimeter is measured in units of length: mm, cm, dm, m, km.

For all polygons, finding the perimeter is reduced to adding the lengths of all sides, that is, the perimeter of a polygon is always equal to the sum of the lengths of its sides. When calculating the perimeter, it is often denoted by a capital Latin letter P:

Square

Area is the part of the plane occupied by a closed flat geometric figure.

Any flat closed geometric figure has a certain area. In the drawings, the area of ​​geometric shapes is the inner region, that is, that part of the plane that is inside the perimeter.

measure area figures - means to find how many times another figure is placed in a given figure, taken as a unit of measurement. Usually, a square is taken as a unit of area measurement, in which the side is equal to the unit of length measurement: millimeter, centimeter, meter, etc.

The figure shows a square centimeter. - a square with each side 1 cm long:

Area is measured in square units of length. Area units include: mm 2, cm 2, m 2, km 2, etc.

Square units conversion table