What is the formula for finding the perimeter. What is a Perimeter? Preparing to learn new material

Perimeter is the sum of the lengths of all sides of the polygon.

• To calculate the perimeter of geometric shapes, special formulas are used, where the perimeter is denoted by the letter "P". It is recommended to write the name of the figure in small letters under the “P” sign, in order to know whose perimeter you are finding.
• Perimeter is measured in units of length: mm, cm, m, km, etc.

Distinctive features of a rectangle

• A rectangle is a rectangle.
• All parallel sides are equal
• All angles = 90º.
• For example, in everyday life, a rectangle can be found in the form of a book, a monitor, a table top or a door.

How to calculate the perimeter of a rectangle

There are 2 ways to find it:

• 1 way. We add all the sides. P = a + a + b + b
• Method 2. Add the width and length, and multiply by 2. P = (a + b) 2. OR P = 2 a + 2 b. The sides of a rectangle that lie opposite each other (opposite) are called length and width.

"A"- the length of the rectangle, the longer pair of its sides.

"B"- the width of the rectangle, the shorter pair of its sides.

An example of a task for calculating the perimeter of a rectangle:

Calculate the perimeter of the rectangle, its width is 3 cm, and its length is 6.

Remember the formulas for calculating the perimeter of a rectangle!

Semi-perimeter is the sum of one length and one width .

• Semi-perimeter of a rectangle - when you perform the first action in brackets - (a + b).
• To get the perimeter from the semi-perimeter, you need to double it, i.e. multiply by 2.

How to find the area of ​​a rectangle

Formula for the area of ​​a rectangle S = a * b

If the length of one side and the length of the diagonal are known in the condition, then the area can be found using the Pythagorean theorem in such problems, it allows you to find the length of the side of a right-angled triangle if the lengths of the other two sides are known.

• : a 2 + b 2 = c 2 where a and b are the sides of the triangle and c is the hypotenuse, the longest side.

Remember!

1. All squares are rectangles, but not all rectangles are squares. Because:
   • Rectangle is a rectangle with all right angles.
   • Square- a rectangle with all sides equal.
2. If you find the area, the answer will always be in square units (mm 2, cm 2, m 2, km 2, etc.)

Surely each of us taught at school such an important component of geometry as the perimeter. Finding the perimeter is essential for many tasks. Our article will tell you how to find the perimeter.

It is worth remembering that the perimeter of any figure is almost always the sum of its sides. Let's take a look at a few different geometric shapes.

1. A rectangle is a quadrilateral in which the parallel sides are equal in pairs. If one side is X and the other is Y, then we get the following formula for finding the perimeter of this figure:

   P = 2 (X + Y) = X + Y + X + Y = 2X + 2Y.

   An example of solving the problem:

   Let's say that side X = 5 cm, side Y = 10 cm. So, substituting these values ​​into our formula, we get - P = 2 * 5 cm + 2 * 10 cm = 30 cm.

2. A trapezoid is a quadrilateral in which two opposite sides are parallel, but not equal to each other. The perimeter of a trapezoid is the sum of all four of its sides:

   P = X + Y + Z + W, where X, Y, Z, W are the sides of the figure.

   An example of solving the problem:

   Let us assume that side X = 5 cm, side Y = 10 cm, side Z = 8 cm, side W = 20 cm. So, substituting these values ​​into our formula, we get - P = 5 cm + 10 cm + 8 cm + 20 cm = 43 cm.

3. The perimeter of a circle (circumference) can be calculated using the formula:

   P = 2rπ = dπ, where r is the radius of the circle, d is the diameter of the circle.

   An example of solving the problem:

   Let's say that the radius r of our circle is 5 cm, then the diameter d will be 2 * 5 cm = 10 cm. It is known that π = 3.14. So, substituting these values ​​into our formula, we get - P = 2 * 5 cm * 3.14 = 31.4 cm.

4. If you need to find the perimeter of a triangle, then you can face a number of problems with this, since triangles can have very different shapes. For example, there are sharp, obtuse, isosceles, right-angled, or equilateral triangles. Although the formula for all types of triangles is:

   P = X + Y + Z, where X, Y, Z are the sides of the figure.

   The problem is that when solving many problems of finding the perimeter of this figure, you will not always know the lengths of all sides. For example, instead of information about the length of one of the sides, you can have the degree of the angle or the length of the height of a particular triangle. This will significantly complicate the task, but will not make its solution unrealistic. How to find the perimeter of a triangle, whatever shape it may be, you can read "".

5. The perimeter of a figure such as a rhombus is found in the same way as the perimeter of a square, because a rhombus is a parallelogram that has equal sides. You can find out how to find the perimeter of a square by reading the article on our website "".

   Now you know how to find the side of the perimeter of the geometric shape that you need!

Perimeter is one of the mathematical, or rather, geometric terms, used mainly to calculate the sides of a figure.

From our article, you will learn what a perimeter is and how it is measured using the example of basic geometric shapes.

Perimeter definition

The perimeter is the total length of all sides or the circumference of a particular figure. The perimeter is denoted by a capital "P", and it can be measured in different units of length, such as millimeters (mm), centimeters (cm), meters (m), etc. For different shapes, there are different formulas for finding the perimeter. Below we will give a few examples of how to find out the perimeter of a rectangle and some other shapes.

We measure the perimeter

If you need to find out the perimeter of a complex figure (such figures include figures with uneven lines), then for this you need a rope or thread. With the help of these things, it is necessary to describe the exact contour of the figure, and in order not to get confused, you can make marks on the rope with a pencil. Or you can just cut it off, and then attach all the parts to the ruler. Thus, you will find out what the perimeter of almost any complex figure is.

There is another device for calculating the perimeter of complex shapes: it is called a curvimeter (roller rangefinder). With its help, you need to set the roller to any point of the shape and describe the outline of the shape with the roller. The resulting number will be equal to the perimeter. You can learn about finding the perimeter of other geometric shapes from our article. Well, we will tell you about several more ways to change the perimeter for different shapes.

Circle, square, equilateral triangle

Let's also take a look at how to find out the perimeter of a circle. It is quite simple: you just need to determine the circumference, and this can be done by multiplying the radius "r" by the number π≈3.14 and then by 2 (P = L = 2 ∙ π ∙ r).

PERIMETER PERIMETER (from the Greek perimetreo - I measure), the length of a closed contour, for example, the sum of the lengths of all sides of a polygon.

Modern encyclopedia. 2000 .

See what "PERIMETER" is in other dictionaries:

Perimeter ... Spelling dictionary-reference

Perimeter 2: New Earth Developer K D Lab Publisher 1C Release Date ... Wikipedia

- (Greek, from peri around, and measuring metreo). The sum of the sides of rectilinear figures. Dictionary of foreign words included in the Russian language. Chudinov AN, 1910. PERIMETER Greek, from peri, around, and metreo, I measure. The circle of the polygon. Explanation ... ... Dictionary of foreign words of the Russian language

Perimeter- the border of the protected area, equipped with physical barriers and checkpoints. A source … Dictionary-reference book of terms of normative and technical documentation

perimeter- a, m. perimètre m., German. Perimeter lat. perimetros circumference peri near + metreo I measure. 1.mate. The sum of the lengths of all sides of a geometric figure. ALS 1. || At that time, St. Laurence plumbing fixtures were installed in wealthy homes. On… … Historical Dictionary of Russian Gallicisms

PERIMETER, the length of the closed contour of a flat figure. The perimeter of a circle is the longest of its CIRCLE. The perimeter of a polygon is equal to the sum of its sides ... Scientific and technical encyclopedic dictionary

PERIMETER, perimeter, husband. (Greek perimetron circle) (mat.). The sum of the lengths of all sides of a flat figure. Perimeter of a triangle. The perimeter of the polygon. Ushakov's explanatory dictionary. D.N. Ushakov. 1935 1940 ... Ushakov's Explanatory Dictionary

Length, border Dictionary of Russian synonyms. perimeter n., number of synonyms: 2 border (39) length ... Synonym dictionary

- (from the Greek perimetreo I measure around) the length of a closed loop, for example. the sum of the lengths of all sides of the polygon ... Big Encyclopedic Dictionary

PERIMETER, ah, husband. In mathematics: the border of a flat figure, as well as the length of that border. | adj. perimetric, oh, oh. Ozhegov's Explanatory Dictionary. S.I. Ozhegov, N.Yu. Shvedova. 1949 1992 ... Ozhegov's Explanatory Dictionary

Books

• PERIMETER - Stuck claw, Sergey Kochetkov. A former submariner, having owed a large sum to a criminal authority, puts his family at risk. To protect her, he embarks on a desperate adventure on the brink of life and treason. His…

, broken line, etc.:

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

Perimeter

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

Any closed geometric figure has a perimeter:

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

The perimeter is measured in length units: 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 is often denoted by the capital letter P:

Square

An area is the portion of a plane that is occupied by a closed planar geometric figure.

Any flat closed geometric figure has a certain area. In the drawings, the area of ​​geometric figures 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 the unit of measurement of area, in which the side is equal to the unit of measurement of length: millimeter, centimeter, meter, etc.

The figure shows a square centimeter. - a square in which each side is 1 cm long:

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

Square unit conversion table