The formula for the area of ​​a rectangle definition entry. How to calculate the area of ​​a rectangle with different sides

Instruction

For example, you that the length of one of the sides (a) is 7 cm, and perimeter rectangle(P) is equal to 20 cm. Since perimeter any figure is equal to the sum of the lengths of its sides, and rectangle opposite sides are equal, then perimeter and will look like this: P = 2 x (a + b), or P = 2a + 2b. From this formula it follows that you can find the length of the second side (b) using a simple operation: b \u003d (P - 2a): 2. So, in our case, side b will be equal to (20 - 2 x 7): 2 \u003d 3 cm .

Now, knowing the lengths of both adjacent sides (a and b), you can substitute them into the area formula S = ab. AT this case rectangle will be equal to 7x3 \u003d 21. Please note that the units of measurement will no longer be, but square centimeters, since you also multiplied the lengths of the two sides of their unit of measurement (centimeters) with each other.

Sources:

  • what is the perimeter of a rectangle

A flat figure consisting of four sides and four right angles. Of all figures square rectangle have to be calculated more often than others. This and square apartments, and square garden area, and square table or shelf surface. For example, to simply wallpaper a room, calculate square its rectangular walls.

Instruction

By the way, from rectangle can be easily calculated square. It is enough to complete the rectangular to rectangle so that the hypotenuse becomes a diagonal rectangle. Then it will be obvious that square such rectangle is equal to the product of the legs of the triangle, and square the triangle itself, respectively, is equal to half the product of the legs.

Related videos

A special case of a parallelogram - a rectangle - is known only in Euclid's geometry. At rectangle All angles are equal, and each of them separately is 90 degrees. Based on private properties rectangle, as well as from the properties of a parallelogram about the parallelism of opposite sides, one can find sides figures along the given diagonals and the angle from their intersection. Side calculation rectangle is based on additional constructions and the application of the properties of the resulting figures.

Instruction

Letter A mark the point of intersection of the diagonals. Consider the EFA formed by the constructions. According to property rectangle its diagonals are equal and bisected by the intersection point A. Calculate the values ​​of FA and EA. Since triangle EFA is isosceles and its sides EA and FA are equal to each other and, respectively, equal to half of the diagonal EG.

Next, calculate the first EF rectangle. This side is the third unknown side of the considered triangle EFA. According to the cosine theorem, use the corresponding formula to find the side EF. To do this, substitute the previously obtained values ​​​​of the sides FА EA and the cosine of the known angle between them α into the cosine formula. Calculate and record the resulting EF value.

Find the other side rectangle FG. To do this, consider another triangle EFG. It is rectangular, where the hypotenuse EG and leg EF are known. According to the Pythagorean theorem, find the second leg FG using the appropriate formula.

Refers to the simplest flat geometric shapes and is one of the special cases of a parallelogram. A distinctive feature of such a parallelogram is the right angles at all four vertices. limited parties rectangle square can be calculated in several ways, using the dimensions of its sides, the diagonals and the angles between them, the radius of the inscribed circle, etc.

Instruction

If the value of the angle (α) that makes up the diagonal is known rectangle on one of its sides, as well as the length (C) of this diagonal, then to calculate the area, you can use the definitions of trigonometric in rectangular. A right triangle here is formed by two sides of a quadrilateral and its diagonal. From the definition of cosine it follows that the length of one of the sides will be equal to the product of the length of the diagonal by the angle, the value is known. From the definition of the sine, you can derive the formula for the length of the other side - it is equal to the product of the length of the diagonal and the sine of the same angle. Substitute these identities into the formula from the previous step, and it turns out that to find the area, you need to multiply the sine and cosine of the known angle, as well as the length of the diagonal rectangle: S=sin(α)*cos(α)*С².

If, in addition to the length of the diagonal (C) rectangle the value of the angle (β) that the diagonals form is known, then one of the trigonometric functions, the sine, can also be used to calculate the area of ​​\u200b\u200bthe figure. Square the length of the diagonal and multiply the result by half the sine of the known angle: S=C²*sin(β)/2.

If (r) is known for a circle inscribed in a rectangle, then to calculate the area, raise this value to the second power and quadruple the result: S = 4 * r². A quadrilateral, in which it is possible, will be a square, and the length of its side is equal to the diameter of the inscribed circle, that is, twice the radius. The formula is obtained by substituting the lengths of the sides, expressed in terms of the radius, into the identity from the first step.

If the lengths (P) and one of the sides (A) are known rectangle, then to find the area inside this perimeter, calculate half the product of the length of the side and the difference between the length of the perimeter and the two lengths of this side: S=A*(P-2*A)/2.

Related videos

The task of finding the perimeter or area of ​​a polygon is not only faced by students in geometry lessons. Sometimes it happens to be solved by an adult. Have you ever had to calculate the required amount of wallpaper for a room? Or maybe you measured the length of the suburban area in order to enclose it with a fence? So knowledge of the basics of geometry is sometimes indispensable for the implementation of important projects.

Using this online calculator, you can find the area of ​​a rectangle.

Using the online calculator for calculating the area of ​​a rectangle, you will receive a detailed step-by-step solution to your example, which will allow you to understand the algorithm for solving such problems and consolidate the material covered.

Entering data into the calculator for calculating the area of ​​a rectangle

You can enter numbers or fractions into the online calculator. Read more in the rules for entering numbers.

N.B. In the online calculator, you can use values ​​in the same units of measurement!

If you have trouble converting units of measure, use the Distance and Length Unit Converter and the Area Unit Converter.

Additional features of the rectangle area calculator

  • You can move between input fields by pressing the right and left keys on the keyboard.

where S is the area of ​​the rectangle,

a is the length of the first side,

b is the length of the second side.

You can enter numbers or fractions (-2.4, 5/7, .). Read more in the rules for entering numbers.

Any obscene comments will be removed and their authors blacklisted!

Copying materials is prohibited.

Welcome to OnlineMSchool.

My name is Dovzhik Mikhail Viktorovich. I am the owner and author of this site, I have written all the theoretical material, as well as developed online exercises and calculators that you can use to study mathematics.

Area of ​​an irregular quadrilateral with given sides

Calculates the area of ​​an irregular quadrilateral with known side lengths

With enviable tenacity, some Planetcalc users leave requests to create a calculator for calculating the area of ​​an irregular quadrilateral, for which only the lengths of the sides are known.

The area of ​​the plot of complex shape

I thought that the only way to stop them was to write such a comic calculator. (Press the "Stop" button to determine the area of ​​the quadrilateral you like with the sides you specified).

Side length A

Side length B

Side length C

Side length D

The area of ​​an irregular quadrilateral, knowing only the lengths of the sides, cannot be calculated. I hope this demo helps anyone who asked for a calculator to understand this.

Why you need to know the floor area
Determining the area of ​​a rectangular room
Calculation of the area of ​​​​the room of the wrong layout
Finding the area of ​​a triangular room

How to calculate the area of ​​​​the walls of a room
Proportions between floor and window area

It is impossible to repair the floor surface without knowing the exact floor area in a private household or apartment. The fact is that today the cost of building materials is quite high, and every property owner tries to save as much as possible on their purchase. Therefore, information on how to calculate the floor area will not be superfluous for someone who prefers to make repairs with his own hands.

Why you need to know the floor area

Before starting work, you should decide on the scope of activities, plan costs and calculate the amount of building materials. To do this, you will need the original data. For this reason, it is important to know how to calculate the floor area accurately. This is especially true for uneven surfaces and rooms with a non-standard layout.

There are other reasons when there is a need to accurately determine the dimensions of the floor surface:

  • checking the quality of construction work;
  • the need for redevelopment of the premises.

Determining the area of ​​a rectangular room

Before you calculate the floor area, you should stock up on a calculator and a measuring tape. Most often there are rooms in the shape of a rectangle. To calculate their area, they use a formula known to everyone from school: S \u003d a x b, where a and b are the length and width. For example, a room has parameters of 3 and 4 meters, then the desired value will be 12 square meters. m.

In the event that the room has a fireplace or built-in furniture, then you need to find out their area and subtract from the total area. In the case of a major overhaul of the floor, all unnecessary in the room will have to be dismantled.

Calculation of the area of ​​​​the room of the wrong layout

It is much more difficult to calculate the area of ​​​​a room that has a polygonal shape. Often in brick houses in the layout there are niches, triangular recesses and rounded elements, as in the photo.

In this case, before calculating the quadrature of the floor, the layout of the room must be divided into separate zones. For example, if the room has an L-shaped layout, it should be divided into 2 rectangles, then calculate the area of ​​\u200b\u200beach of them and add the results.

Finding the area of ​​a triangular room

When another part of the room is not perpendicular to the main area, this means that there is also a triangle between the two rectangles, which has a right angle.

In this case, the area of ​​the triangle is calculated by the formula: S \u003d (a x b): 2 and added to the grand total. For example, a \u003d 2, b \u003d 3, then S \u003d (2x3): 2 \u003d 3 m².

You can define the area in another way:

  1. First calculate the square of the rectangle.
  2. Determine the area of ​​the beveled triangular corner.
  3. Subtract the area of ​​the triangle from the quadrature of the rectangle.

In the case when the triangle does not have a right angle, then use the Heron formula S \u003d √p (p - a) (p - b) (p - c).

For example, its sides are 5, 6 and 7 meters, then the calculations are made as follows:

  1. Find out the semiperimeter of the triangle p = (5+6+7):2 = 9.
  2. Digital values ​​​​are substituted into the Heron formula and the result is obtained: √ (9 x (9-7) x (9-6) x (9-5) \u003d 14.7 m².

The square of the premises is rounded

Often, a similar form is present at the windows in old houses or on balconies that are combined with rooms. First, calculate 1/2 of the protruding part of the circle and add to the area of ​​the rectangle, applying the formula S = πR²: 2, in which:

R² is the radius of the circle squared.

For example, the room has a protruding semi-circular balcony with a radius of 1.5 meters. Substituting this number into the formula, we get the result: S \u003d 3.14x (1.5)²: 2 \u003d 3.5 m². See also: "How to calculate the square meters of the floor with different shapes of rooms."

How to calculate the area of ​​​​the walls of a room

The procedure for calculating the area of ​​\u200b\u200bwalls and floor is different. The fact is that before you calculate the quadrature of the floor, you should find out the length and width of the room, and to calculate the walls you will need to measure its height. Therefore, they first find out the perimeter of the room and multiply by the height of the ceilings.

For example, the floor parameters are 3 and 4 meters, and the height of the room is 3 meters. In this case, the perimeter of the walls will be equal to (3 + 4) x2 = 14 m, and their area S = 14x3 = 42 m².
In this case, one should not forget about the quadrature of the openings of windows and doors. Their area is subtracted after the completion of wall calculations. But on the other hand, they can be ignored and thus provide a certain supply of materials.

Proportions between floor and window area

According to SNiP 31-01-2003, the parameters of windows and their number should depend on the quadrature of the floor. So for residential multi-apartment buildings, the ratio between the areas of window openings and the floor surface will be from 1:5.5 to 1:8. As for the upper floors, a minimum proportion of 1:10 is allowed there.

For private households, this norm is regulated by SNiP 31-02-2001.

How to calculate the area of ​​a rectangle with different sides

According to this documentation, for every 8 "squares" of the floor surface, there must be at least one "square" of a source of natural light flux. On the attic floors, this proportion cannot be less than 1:10.

To ensure high-quality repairs, you need to find out in advance how to calculate the floor area and other necessary dimensions of the room. The preparatory stage also provides for the purchase of building materials and then during the repair process, costs will be minimized, since there will not be large residues and the cost of delivery will be inexpensive.

The manual method of calculating how to find out the floor area will take longer than when making calculations on an existing building calculator, but it allows you to find out more accurate results.

How to calculate the area of ​​a rectangle

Area formulas

Geometric area- the part of the surface bounded by the closed contour of the given figure. The size of the area is expressed by the number of square units contained in it.

Triangle area formulas

1st formula

S- area of ​​a triangle

a, b- lengths of 2 sides of a triangle

With is the angle between sides a and b

2nd formula

S- area of ​​a triangle

a- the length of the side of the triangle

h- the length of the height lowered to side a

3d formula

S- area of ​​a triangle

a, b, c

p- semiperimeter of a triangle

4th formula

S- area of ​​a triangle

r- radius of the inscribed circle

p- semiperimeter of a triangle

5th formula

S- area of ​​a triangle

a, b, c- lengths of 3 sides of a triangle

R is the radius of the circumscribed circle

See also: Program for calculating the area of ​​a triangle.

Square area formulas:

1) The area of ​​a square is equal to the square of the length of its side (a).

2) The area of ​​a square is half the square of the length of its diagonal (d).

S- square area

a- side length of the square

d is the length of the diagonal of the square

See also: Program for calculating the area of ​​a square.

Rectangle area formula:

1) The area of ​​a rectangle is equal to the product of the lengths of its two adjacent sides (a, b).

S- area of ​​the rectangle

a- length of the 1st side of the rectangle

b- length of the 2nd side of the rectangle

See also: Program for calculating the area of ​​a rectangle.

Parallelogram area formula:

1) The area of ​​a parallelogram is equal to the product of the length of its base and the length of its height (a, h).

S is the area of ​​the parallelogram

a- base length

h- height length

See also: Program for calculating the area of ​​a parallelogram.

Trapezoid area formula:

1) The area of ​​a trapezoid is equal to the product of half the sum of its bases and the height (a, b, h).

S- area of ​​the trapezoid

a- length of the 1st base

b- length of the 2nd base

h- the length of the height of the trapezoid

Calculator for calculating the area of ​​a land plot of irregular shape with different sides

See also: Program for calculating the area of ​​a trapezoid.

Formulas for the area of ​​a rhombus:

1) The area of ​​a rhombus is equal to the product of the length of its side and the height (a, h).

2) The area of ​​a rhombus is half the product of its diagonals.

S- area of ​​a rhombus

a- length of the base of the rhombus

h- the length of the height of the rhombus

d1- length of the 1st diagonal

d2- length of the 2nd diagonal

See also: Program for calculating the area of ​​a rhombus.

Circle area formula:

1) The area of ​​a circle is equal to the product of the square of the radius and the number pi (3.1415).

2) The area of ​​a circle is equal to half the product of the length of the circle bounding it and the radius.

S- area of ​​a circle

π - pi (3.1415)

r- circle radius

See also: Program for calculating the area of ​​a circle.

Ellipse area formula:

1) The area of ​​the ellipse is equal to the product of the lengths of the major and minor semiaxes of the ellipse and the number pi (3.1415).

S- area of ​​the ellipse

π - pi (3.1415)

a- the length of the major semi-axis

b- the length of the minor semiaxis

See also: Program for calculating the area of ​​an ellipse.

Online calculator. Rectangle area

Briefly about the main entry level

Square figures on checkered paper. First level.

The algorithm for finding the area of ​​\u200b\u200bfigures on checkered paper:

  1. Subtract the sum of the areas of all extra shapes from the area of ​​the rectangle.

How to find the area of ​​\u200b\u200bfigures on checkered paper:

Method 1: (useful for standard shapes: triangle, trapezoid, etc.)

  1. By counting the cells and applying simple theorems, find those sides, heights, diagonals that are required to apply the area formula.
  2. Substitute the found values ​​into the area equation.

Method 2: (very convenient for complex shapes, but not bad for simple ones)

  1. Complete the desired figure to a rectangle.
  2. Find the area of ​​all the resulting additional shapes and the area of ​​the rectangle itself.
  3. Subtract the sum of the areas of all extra shapes from the area of ​​the rectangle.

Illustrate first way.

Let you need to find the area of ​​such a trapezoid built on a sheet in a cage

We just count the cells and see that in our case, and. Substitute in the formula:

It seems to be even rectangular and, but what is equal to, and what is equal to? How to find out? Let's use both methods for complete clarity.

I way.

Substitute in the formula:

II way(I'll tell you a secret - this way is better).

We need to surround our figure with a rectangle. Like this:

It turned out one (necessary) triangle inside and as many as three unnecessary triangles outside. But on the other hand, the areas of these unnecessary triangles are easily calculated on a sheet in a cage! Here we will count them, and then simply subtract from the whole rectangle.

Why is this way better? Because it works for the most cunning figures too. Look, you need to calculate the area of ​​\u200b\u200bsuch a figure:

We surround it with a rectangle and again we get one necessary, but complex area and many unnecessary, but simple ones.

And now, to find the area, we simply find the area of ​​\u200b\u200bthe rectangle and subtract from it the remaining area of ​​\u200b\u200bthe figures on checkered paper.

(note that the area is NOT a right triangle, but it is still easy to calculate by the basic formula).

Here is the answer: .

Well, how do you like this method? Try to use it always, and you can easily find the area of ​​\u200b\u200bthe figures on checkered paper!

Lesson on the topic: "Formulas for determining the area of ​​a triangle, rectangle, square"

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Teaching aids and simulators in the online store "Integral" for grade 5
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Definition and concept of the area of ​​\u200b\u200ba figure

To better understand what the area of ​​\u200b\u200bthe figure is, consider the figure.
This arbitrary figure is divided into 12 small squares. The side of each square is 1 cm. And the area of ​​each square is 1 square centimeter, which is written as follows: 1 cm2.

Then the area of ​​the figure is 12 square centimeters. In mathematics, area is denoted by the Latin letter S.
So the area of ​​our figure is: S figures \u003d 12 cm 2.

The area of ​​the figure is equal to the area of ​​all the small squares of which it consists!

Guys, remember!
Area is measured in square units of length. Area units:
1. Square kilometer - km 2 (when the areas are very large, for example, a country or a sea).
2. Square meter - m 2 (quite suitable for measuring the area of ​​\u200b\u200ba plot or apartment).
3. Square centimeter - cm 2 (usually used in mathematics lessons when drawing figures in a notebook).
4. Square millimeter - mm 2.

Area of ​​a triangle

Consider two types of triangles: rectangular and arbitrary.

To find the area of ​​a right triangle, you need to know the length of the base and the height. In a right triangle, one of the sides replaces the height. Therefore, in the formula for the area of ​​a triangle, instead of the height, we substitute one of the sides.
In our example, the sides are 7 cm and 4 cm. The formula for calculating the area of ​​a triangle is written as follows:
S of right triangle ABC = BC * SA: 2


S of a right triangle ABC \u003d 7 cm * 4 cm: 2 \u003d 14 cm 2

Now consider an arbitrary triangle.

For such a triangle, it is necessary to draw the height to the base.
In our example, the height is 6 cm, and the base is 8 cm. As in the previous example, we calculate the area using the formula:
S of an arbitrary triangle ABC = BC * h: 2.

Substitute our data into the formula and get:
S of an arbitrary triangle ABC \u003d 8 cm * 6 cm: 2 \u003d 24 cm 2.

Area of ​​rectangle and square

Take a rectangle ABCD with sides 5 cm and 8 cm.
The formula for calculating the area of ​​a rectangle is:
S rectangle ABCD = AB * BC.


S rectangle ABCD \u003d 8 cm * 5 cm \u003d 40 cm 2.

Now let's calculate the area of ​​the square. Unlike a rectangle and a triangle, to find the area of ​​a square, you need to know only one side. In our example, the side of the square ABCD is 9 cm. S of the square ABCD \u003d AB * BC \u003d AB 2.

Substitute our data into the formula and get:
S square ABCD \u003d 9 cm * 9 cm \u003d 81 cm 2.

With such a concept as the area, we have to deal with in our lives every day. So, for example, when building a house, you need to know it in order to calculate the amount of material needed. The size of the garden plot will also be characterized by the area. Even repairs in an apartment cannot be done without this definition. Therefore, the question of how to find the area of ​​a rectangle on our life path arises very often and is important not only for schoolchildren.

For those who don't know, a rectangle is a flat figure with opposite sides equal and angles 90°. To denote the area in mathematics, the English letter S is used. It is measured in square units: meters, centimeters, and so on.

Now let's try to give a detailed answer to the question of how to find the area of ​​a rectangle. There are several ways to determine this value. Most often, we are faced with a way to determine the area using width and length.

Let's take a rectangle with width b and length k. To calculate the area of ​​a given rectangle, multiply the width by the length. All this can be represented in the form of a formula that will look like this: S \u003d b * k

Now let's look at this method with a specific example. It is necessary to determine the area of ​​\u200b\u200bthe garden plot with a width of 2 meters and a length of 7 meters.

S = 2 * 7 = 14 m2

In mathematics, especially in high school, we have to determine the area in other ways, since in many cases we do not know either the length or the width of the rectangle. At the same time, there are other known quantities. How to find the area of ​​a rectangle in this case?

If we know the length of the diagonal and one of the angles that makes up the diagonal with any side of the rectangle, then in this case we need to remember the area of ​​the right triangle. After all, if you look, then the rectangle consists of two equal right-angled triangles. So, back to the defined value. First you need to determine the cosine of the angle. Multiply the resulting value by the length of the diagonal. As a result, we get the length of one of the sides of the rectangle. Similarly, but already using the definition of the sine, you can determine the length of the second side. How to find the area of ​​a rectangle now? Yes, it is very simple to multiply the obtained values.

In formula form, it would look like this:

S = cos(a) * sin(a) * d2 , where d is the length of the diagonal

Another way to determine the area of ​​a rectangle is through a circle inscribed in it. It applies if the rectangle is a square. To use this method, you need to know the radius of the circle. How to calculate the area of ​​a rectangle in this way? Of course, according to the formula. We will not prove it. And it looks like this: S = 4 * r2, where r is the radius.

It happens that instead of the radius, we know the diameter of the inscribed circle. Then the formula will look like this:

S=d2, where d is the diameter.

If one of the sides and the perimeter are known, then how to find out the area of ​​the rectangle in this case? To do this, you need to make a number of simple calculations. As we know, the opposite sides of a rectangle are equal, so the known length, multiplied by two, must be subtracted from the perimeter value. Divide the result by two and get the length of the second side. Well, then the standard trick, we multiply both sides and get the area of ​​the rectangle. In formula form, it would look like this:

S=b* (P - 2*b), where b is the length of the side, P is the perimeter.

As you can see, the area of ​​a rectangle can be determined in various ways. It all depends on what quantities we know before considering this issue. Of course, the latest calculus methods are practically never found in life, but they can be useful for solving many problems at school. Perhaps this article will be useful for solving your problems.

We already knew fi-gu-ry area, did you find out one of the units from the me-re-niya area - square meter. In the lesson, we-we-we-we-we-we-we-lo, how do you-number-pour the area of ​​a rectangle-mo-coal-no-ka.

We already know how to find an area of ​​​​figures, some times-de-le-na into square san-ti-meters.

For example:

We can determine that the area of ​​the first fi-gu-ra is 8 cm2, the area of ​​the second fi-gu-ra is 7 cm2.

How to find the area of ​​a rectangle-mo-coal-no-ka, the lengths of the sides of something-ro-go 3 cm and 4 cm?

To solve the problem of da chi, we break the rectangle-coal-nick into 4 los-ki of 3 cm2 each.

Then the area of ​​the rectangle will be equal to 3 * 4 = 12 cm2.

The same rectangle-nick can be broken into 3 strips of 4 cm2 each.

Then the area of ​​the rectangle will be equal to 4 * 3 = 12 cm2.

In both cases, for finding the square, it’s right-mo-coal-no-re-re-multiple numbers, you-ra-zh-yu- the lengths of the sides of the rectangle are mo-coal-no-ka.

Find the area of ​​\u200b\u200beach rectangle.

Ras-look at the rectangle-coal-nickname AKMO.

There are 6 cm2 in one layer, and there are 2 such ones in this rectangle. So, we can do the following Action:

The number 6 means the length of the rectangle, and 2 - shi-ri-well, the rectangle-no-ka. In this way, we re-multiple a hundred rectangles in order to find the square of a rectangle.

Ras-look at the rectangle KDCO.

In a rectangle-mo-coal-no-ke KDCO in one layer 2 cm2, and there are 3 such lo-juice.

The number 3 means the length of the rectangle, and 2 - shi-ri-well, the rectangle-no-ka. We re-multiple them and found out the area is right-coal-no-ka.

We can conclude: to find the area of ​​\u200b\u200brectangular-coal-no-ka, you don’t need to break fi-gu-ru every time into square san-ti-meters.

In order to calculate the area of ​​a rectangle-mo-coal-no-ka, you need to find its length and shi-ri-nu (the lengths of the sides of a rectangle-mo-coal-no-ka should be you-ra -zhen-us in the same units from-me-re-niya), and then calculate-to-pour pro-from-ve-de-nie on-beam-chen-ny numbers (flat- mercy will be you-ra-same-on in co-ot-vet-stvo-yu-shchi edi-ni-tsakh area)

To generalize: the square of a rectangle-mo-coal-no-ka is equal to the pro-of-ve-de-nyu of its length and width.

Re-shi-te for-da-choo.

Are you numbering the square of a right-coal-no-ka, if the length of the right-coal-no-ka is 9 cm, and the width is 2 cm.

Ras-jug-yes-eat like that. In this task, from the West, both the length and the shi-ri-on a right-coal-no-ka. In this way, we act according to the right: the area of ​​\u200b\u200bthe rectangle is equal to the pro-of-ve-de-ny of its length and width.

For-we-we-we-re-she-nie.

Answer: square square-mo-coal-no-ka 18cm2

How do you think, what else can be the lengths of the sides of a rectangle with such an area?

You can argue like this. Since the area is about the lengths of the sides of the right-coal-no, so you need to remember the tab-li-tsu smartly -tion. When multiplying, what numbers do you think the answer is 18?

It’s right, when you multiply 6 and 3, it’s also 18. It means that a rectangle can have sides of 6 cm and 3 cm and its area will also be equal to 18cm2.

Re-shi-te for-da-choo.

The length of the rectangle is 8 cm, and the width is 2 cm. Find its area and peri-meter.

We know the length and shi-ri-on a rectangle-mo-coal-no-ka. It is necessary to remember the thread that for finding the area, it is necessary to find a pro-of-ve-de-tion of its length and width , and for finding-de-niya pe-ri-meter, you need the sum of the length and width-ri-ny multiplied by two.

For-we-we-we-re-she-nie.

Answer: the square of the rectangle is 16 cm2, and the perimeter of the rectangle is 20 cm.

Re-shi-te for-da-choo.

The length of the rectangle is 4 cm, and the width is 3 cm. What is the area of ​​a triangular-no-ka? (See ri-su-nok)

In order to answer the question for-da-chi, sna-cha-la, you need to find an area of ​​\u200b\u200brect-coal-no-ka. We know that for this it is necessary to multiply the length by shi-ri-nu.

Look at the devil. Are you for-me-ti-whether, dia-go-nal once-de-li-la a right-mo-angle-nick into two equal triangles-no-ka? Next, the area of ​​one triangle is 2 times smaller than the square of a right-coal-no-ka. So, it is necessary to reduce 12 by 2 times.

Answer: the area of ​​\u200b\u200bthe triangle is 6 cm2.

This year, in the lesson, we got to know the right, how to calculate the area of ​​​​rectangular-coal-no-ka and learned to use to take this right-vi-lo when solving problems on the na-hod-de-square square right-mo-coal-no-ka.

SOURCES

http://interneturok.ru/ru/school/matematika/3-klass/tema/ploschad-pryamougolnika?seconds=0&chapter_id=1779