Calculating the perimeter of a square is an important skill. AND we're talking about not just about schoolwork. After all, with the help of simple mathematical operations you can easily calculate the amount of building material needed. For example, to install a fence around the perimeter of a square plot or wallpaper in a square room.
To find the perimeter of a square, you need to know the value of one of the sides, the area or the radius of the circumscribed circle. Let's consider these methods in more detail.
How to find the perimeter of a square given one side of the square
- The perimeter of a figure is the sum of all its sides. Since a square has only 4 sides, its perimeter is:
P = a + b + c + d,
where P is the perimeter,
a, b, c, d - sides. - Knowing that all sides of a square are equal, we simplify the formula:
P = 4a,
where a is one of the sides,
4 is the sum of the sides. - Example solution: if the side is 7, then
P = 4*7 = 28.
How to find the perimeter of a square given the area of the square
- The area of the square is calculated by the formula:
S = a*a = a²,
where S is the area,
a - any side. - Let's rewrite the formula:
a² = S,
a = √S.
Example solution: if the area is 121, then
a = √121 = 11. - Knowing the side of the square, we can find the perimeter:
P = 4*a. - Example solution: P = 4*11 = 44.
How to find the perimeter of a square given the radius of the circumscribed circle
Suppose we are given a square and know the radius of the circle that describes it on all sides. If we draw a diagonal between the opposite corners of the square, we get 2 triangles with right angles. In this case, it would be a sin not to use the Pythagorean theorem, which states: “The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.”
What else do we know:
- The sides b and c of the 2 triangles are equal, since these are the sides of a square. They are also legs.
- Triangles have a common hypotenuse a, which is also the diameter of the circle.
- The diameter is equal to two radii (2r).
Let's start finding the perimeter:
- According to the Pythagorean theorem:
b² + c² = a²,
where in and c are legs right triangle,
a is the hypotenuse. - Knowing that a (hypotenuse) = 2r, and b = c, we simplify the formula:
в² + в² = (2r)²,
2в² = 4(r)², reduce by 2:
in² = 2(r)²,
в = √2r, where
c is the side of the square. - Since the perimeter of a square equal to the sum sides, let's modify the formula:
Р = 4√2r,
where P is the desired perimeter,
4 - sum of sides,
√2r - side length. - Let's simplify the formula:
Р = 4√2 * 4√r,
P = 5.657r,
where P is the desired perimeter,
r is the radius of the circle.
Example solution:
If the radius of the circle is 20:
P = 5.657*20 = 113.14.
The numbers are quickly forgotten, but the problem can always be solved using the Pythagorean theorem:
in² + in² = (2*20)²,
2в² = 40²,
2в² = 1600, divide by 2:
in² = 800,
in = √800,
in = 28.28,
where in is one side.
So,
P = 4*28.29,
P = 113.14.
There are many ways to find the perimeter of a square, but they all boil down to the fact that the perimeter is equal to the sum of all sides.
A square is a positive quadrilateral (or rhombus) in which all angles are right and the sides are equal. Like any other regular polygon, square allowed to calculate perimeter and area. If area square already famous, then discover its sides, and after that perimeter won't be difficult.
Instructions
1. Square square is found by the formula: S = a? This means that in order to calculate the area square, you need to multiply the lengths of its 2 sides by each other. As a consequence, if you know the area square, then when extracting the root from a given value, you can find out the length of the side square.Example: area square 36 cm?, in order to find out the side of this square, need to be extracted Square root from the area value. Thus, the length of the side of a given square 6 cm
2. To find perimeter A square you need to add up the lengths of all its sides. With the help of a formula, this can be expressed as follows: P = a+a+a+a. If you take the root of the area value square, and after that add the resulting value 4 times, then you can detect perimeter square .
3. Example: Given a square with an area of 49 cm?. Need to discover it perimeter.Solution: First you need to extract the root of the area square: ?49 = 7 cmThen, calculating the length of the side square, it is possible to calculate and perimeter: 7+7+7+7 = 28 cmAnswer: perimeter square area 49 cm? is 28 cm
Often in geometric problems It is required to find the side length of a square if its other parameters are known - such as area, diagonal or perimeter.
You will need
- Calculator
Instructions
1. If the area of a square is known, then in order to find the side of the square, you need to take the square root of the numerical value of the area (because the area of the square is equal to the square of its side): a =? S, where a is the length of the side of the square; S is the area of the square. Unit measuring the side of a square will be a linear unit of length, corresponding to a unit of area. Say, if the area of a square is given in square centimeters, then the length of its side will be primitively in centimeters. Example: The area of a square is 9 square meters. Find the length of the side of the square. Solution: a =? 9 = 3 Answer: The side of a square is 3 meters.
2. In the case when the perimeter of the square is known, to determine the length of the side it is necessary to divide the numerical value of the perimeter by four (because the square has four sides of identical length): a = P/4, where: a is the length of the side of the square; P is the perimeter of the square. The unit of measurement for the side of a square will be the same linear unit of length as the perimeter. Say, if the perimeter of a square is given in centimeters, then the length of its side will also be in centimeters. Example: The perimeter of a square is 20 meters. Find the length of the side of the square. Solution: a = 20/4 = 5 Answer: The length of the side of the square is 5 meters.
3. If the length of the diagonal of a square is known, the length of its side will be equal to the length of its diagonal divided by the square root of 2 (by the Pythagorean theorem, because the adjacent sides of the square and the diagonal make up a rectangular isosceles triangle):a=d/?2 (since a^2+a^2=d^2), where: a is the length of the side of the square; d is the length of the diagonal of the square. The unit of measurement for the side of the square will be the unit of measurement for the length the same as the diagonal. Say, if the diagonal of a square is measured in centimeters, then the length of its side will be in centimeters. Example: The diagonal of a square is 10 meters. Find the length of the side of the square. Solution: a = 10/?2, or approximately: 7.071 Answer: The length of the side of the square is 10/?2, or approximately 1.071 meters.
A square is a beautiful and simple flat geometric figure. This is a rectangle with equal sides. How to detect perimeter square, if the length of its side is known?
Instructions
1. Before everyone else, it is worth remembering that perimeter is nothing more than the sum of the lengths of the sides of a geometric figure. The square we are considering has four sides. Moreover, by definition square, all these sides are equal to each other. From these premises follows a simple formula for finding perimeter A square – perimeter square equal to length sides square, multiplied by four: P = 4a, where a is the length of the side square .
Video on the topic
The perimeter is called the universal length The boundaries of the figure are more frequent than each one on the plane. A square is a positive quadrilateral or a rhombus in which all angles are right, or a parallelogram in which all sides and angles are equal.
You will need
- Knowledge of geometry.
Instructions
1. Perimeter square equal to the sum of the lengths of its sides. Because a square, in its essence, is a quadrilateral, it has four sides, which means the perimeter is equal to the sum of the lengths of the four sides or P = a+b+c+d.
2. A square, as can be seen from the definition, is a regular geometric figure, which means that all its sides are equal. So a=b=c=d. Consequently, P = a+a+a+a or P = 4*a.
3. Let the side square is equal to 4, that is, a=3. Then the perimeter or length square, according to the resulting formula, will be equal to P = 4*3 or P=12. The number 12 will be the length or, which is the same thing, the perimeter square .
Video on the topic
Note!
The perimeter of a square is invariably the correct value, like any other length.
Helpful advice
In a similar way, it is possible to determine the perimeter of a rhombus, because a square is a special case of a rhombus with right angles.
The perimeter characterizes the length of the closed silhouette. Like the area, it can be detected using other quantities given in the problem statement. Problems on finding the perimeter are extremely common in school mathematics courses.
Instructions
1. Knowing the perimeter and side of a figure, you can discover its other side, as well as its area. The perimeter itself, in turn, can be detected along several specified sides or along an angle and sides, depending on the conditions of the problem. Also in some cases it is expressed through area. The perimeter of a rectangle is especially primitive. Draw a rectangle with one side equal to a and a diagonal equal to d. Knowing these two quantities, use the Pythagorean theorem to find its other side, which is the width of the rectangle. Having found the width of the rectangle, calculate its perimeter as follows: p=2(a+b). This formula is objective for all rectangles, since each of them has four sides.
2. Pay attention to the fact that in most problems the perimeter of a triangle is found only if there is information about only one of its angles. However, there are also problems in which all the sides of the triangle are known, and then the perimeter can be calculated by simple summation, without the use of trigonometric calculations: p=a+b+c, where a, b and c are the sides. But such problems are rarely found in textbooks, because the method for solving them is clear. Solve more difficult problems of finding the perimeter of a triangle step by step. Let's say, draw an isosceles triangle whose base and angle are known. In order to find its perimeter, first find sides a and b as follows: b=c/2cos?. From the fact that a=b (isosceles triangle), make a further result: a=b=c/2cos?.
3. Calculate the perimeter of the polygon in a similar way, adding the lengths of all its sides: p=a+b+c+d+e+f and so on. If the polygon is positive and inscribed in a circle or described around it, calculate the length of one of its sides, and then multiply by their number. Let's say, in order to find the sides of a hexagon inscribed in a circle, proceed as follows: a=R, where a is the side of the hexagon equal to the radius of the circumscribed circle. Accordingly, if the hexagon is correct, then its perimeter is equal to: p=6a=6R. If a circle is inscribed in a hexagon, then the side of the latter is equal to: a=2r?3/3. Accordingly, find the perimeter of such a figure in the following way: p=12r?3/3.
Although the word “perimeter” comes from the Greek designation for a circle, it is customary to refer to the total length of the boundaries of any flat geometric figure, including a square. Calculating this parameter, as usual, is not difficult and can be carried out using several methods, depending on the known initial data.
Instructions
1. If you know the length of the side of the square (t), then to find its perimeter (p), simply increase this value by four times: p=4*t.
2. If the length of the side is unknown, but in the conditions of the problem the length of the diagonal (c) is given, then this is enough to calculate the length of the sides, and consequently the perimeter (p) of the polygon. Use the Pythagorean theorem, which states that the square of the length of the long side of a right triangle (the hypotenuse) is equal to the sum of the squares of the lengths of the short sides (the legs). In a right triangle, composed of 2 adjacent sides of a square and the extreme points of a segment connecting them, the hypotenuse coincides with the diagonal of the quadrilateral. It follows from this that the length of the side of a square is equal to the ratio of the length of the diagonal to the square root of two. Use this expression in the formula to calculate the perimeter from the previous step: p=4*c/?2.
3. If only the area (S) of a section of the plane limited by the perimeter of the square is given, then this will be enough to determine the length of one side. Because the area of any rectangle is equal to the product of the lengths of its adjacent sides, then to find the perimeter (p) take the square root of the area, and quadruple the total: p=4*?S.
4. If the radius of the circle described near the square is known (R), then to find the perimeter of the polygon (p), multiply it by eight and divide the resulting total by the square root of two: p=8*R/?2.
5. If the circle whose radius is inscribed in a square, then calculate its perimeter (p) by simply multiplying the radius (r) by eight: P=8*r.
6. If the square in question in the problem conditions is described by the coordinates of its vertices, then to calculate the perimeter you will need data on only 2 vertices belonging to one of the sides of the figure. Determine the length of this side, based on the same Pythagorean theorem for a triangle composed of itself and its projections on the coordinate axes, and increase the resulting total by four times. Because the lengths of the projections onto the coordinate axes are equal to the modulus of the differences corresponding coordinates 2 points (X?;Y? and X?;Y?), then the formula can be written as follows: p=4*?((X?-X?)?+(Y?-Y?)?).
In general, the perimeter is the length of the line that limits a closed figure. For polygons, the perimeter is the sum of all side lengths. This value can be measured, and for many figures it can be easily calculated if the lengths of the corresponding elements are known.
You will need
- – ruler or tape measure;
- – strong thread;
- – roller rangefinder.
Instructions
1. To measure the perimeter of an arbitrary polygon, use a ruler or other measuring device to measure all its sides, and then find their sum. If given a quadrilateral with sides of 5, 3, 7 and 4 cm, which are measured with a ruler, find the perimeter by adding them together P=5+3+7+4=19 cm.
2. If the figure is arbitrary and includes more than just straight lines, then measure its perimeter with a traditional rope or thread. To do this, position it so that it correctly follows all the lines limiting the figure, and make a mark on it; if possible, trim it roughly to avoid confusion. After this, using a tape measure or ruler, measure the length of the thread, it will be equal to the perimeter of this figure. Be sure to ensure that the thread follows the line as accurately as possible for greater accuracy of the result.
3. Measure the perimeter of a difficult geometric figure with a roller range finder (curvimeter). To do this, a point is marked on the line at which the rangefinder roller is installed and rolled along it until it returns to starting point. The distance measured by the roller rangefinder will be equal to the perimeter of the figure.
4. Perimeter of some geometric shapes calculate. Say, in order to find the perimeter of any positive polygon (a convex polygon whose sides are equal), multiply the length of the side by the number of angles or sides (they are equal). In order to find the perimeter of a regular triangle with a side of 4 cm, multiply this number by 3 (P = 4? 3 = 12 cm).
5. To find the perimeter of an arbitrary triangle, add up the lengths of all its sides. If all sides are not given, but there are angles between them, find them using the sine or cosine theorem. If two sides of a right triangle are known, find the third using the Pythagorean theorem and find their sum. Let's say, if it is known that the legs of a right triangle are equal to 3 and 4 cm, then the hypotenuse will be equal to?(3?+4?)=5 cm. Then the perimeter P=3+4+5=12 cm.
6. To find the perimeter of a circle, find the circumference that limits it. To do this, multiply its radius r by the number??3.14 and the number 2 (P=L=2???r). If the diameter is known, consider that it is equal to two radii.
Perimeter polygon called a closed broken line made up of all its sides. Finding the length of this parameter comes down to summing the lengths of the sides. If all the segments forming the perimeter of such a two-dimensional geometric figure have identical dimensions, the polygon is called true. In this case, calculating the perimeter is much simpler.
Instructions
1. In the simplest case, when the length of side (a) of the correct polygon and the number of vertices (n) in it, to calculate the length of the perimeter (P), simply multiply these two quantities: P = a*n. Let's say the perimeter length of a regular hexagon with a side of 15 cm should be equal to 15 * 6 = 90 cm.
2. Calculate the perimeter of such polygon along the known radius (R) of the circle described around it is also permissible. To do this, you will first have to express the length of the side using the radius and the number of vertices (n), and then multiply the resulting value by the number of sides. To calculate the side length, multiply the radius by the sine of Pi divided by the number of vertices, and double the total: R*sin(?/n)*2. If you are more comfortable calculating the trigonometric function in degrees, replace Pi with 180°: R*sin(180°/n)*2. Calculate the perimeter by multiplying the resulting value by the number of vertices: P = R*sin(?/n)*2*n = R*sin(180°/n)*2*n. Say, if a hexagon is inscribed in a circle with a radius of 50 cm, its perimeter will have a length of 50*sin(180°/6)*2*6 = 50*0.5*12 = 300 cm.
3. A similar method allows you to calculate the perimeter without knowing the length of the positive side polygon, if it is described around a circle with a famous radius (r). In this case, the formula for calculating the size of the side of the figure will differ from the previous one only involved trigonometric function. Replace the sine with the tangent in the formula to get the following expression: r*tg(?/n)*2. Or for calculations in degrees: r*tg(180°/n)*2. To calculate the perimeter, increase the resulting value by a number of times equal to the number of vertices polygon: P = r*tg(?/n)*2*n = r*tg(180°/n)*2*n. Let's say, the perimeter of an octagon described near a circle with a radius of 40 cm will be approximately equal to 40*tg(180°/8)*2*8? 40*0.414*16 = 264.96 cm.
A square is a geometric figure consisting of four sides of identical length and four right angles, each of which is equal to 90°. Determination of area or perimeter quadrilateral, and any quadrilateral, is required not only when solving problems in geometry, but also in Everyday life. This knowledge can become useful, say, during repairs when calculating the required number of materials - coverings for floors, walls or ceilings, as well as for laying out lawns and beds, etc.
Instructions
1. To determine the area of a square, multiply the length by the width. Because in a square the length and width are identical, then the value of one side is enough to be squared. Thus, the area of a square is equal to the length of its side squared. The unit of measurement for area can be square millimeters, centimeters, decimeters, meters, kilometers. To determine the area of a square, you can use the formula S = aa, where S – area of the square, a- side of a square.
2. Example No. 1. The room is shaped like a square. How much laminate (in sq.m) will be needed to completely cover the floor if the length of one side of the room is 5 meters. Write down the formula: S = aa. Substitute the data specified in the condition into it. Because a = 5 m, therefore, the area will be equal to S (rooms) = 5x5 = 25 sq.m, which means S (laminate) = 25 sq.m.
3. The perimeter is the total length of the shape's border. In a square, the perimeter is the length of all four, and identical, sides. That is, the perimeter of a square is the sum of all its four sides. To calculate the perimeter of a square, it is enough to know the length of one of its sides. The perimeter is measured in millimeters, centimeters, decimeters, meters, kilometers. To determine the perimeter there is a formula: P = a + a + a + a or P = 4a, where P is the perimeter, a is the length of the side.
4. Example No. 2. For finishing works Square-shaped rooms require ceiling plinths. Calculate the total length (perimeter) of the baseboards if the size of one side of the room is 6 meters. Write down the formula P = 4a. Substitute the data specified in the condition into it: P (rooms) = 4 x 6 = 24 meters. Consequently, the length of the ceiling plinths will also be equal to 24 meters.
Video on the topic
Note!
The following definitions are objective for a square: A square is a rectangle, one that has sides equal to each other. A square is a special type of rhombus in which all of the angles are equal to 90 degrees. Being a positive quadrilateral, a circle can be described or inscribed around a square. The radius of a circle inscribed in a square can be found using the formula: R = t/2, where t is the side of the square. If the circle is circumscribed around it, then its radius is found as follows: R = (?2*t)/2 Based on these formulas, it is possible derive new ones to find the perimeter of a square: P = 8*R, where R is the radius of the inscribed circle; P = 4*?2*R, where R is the radius of the inscribed circle. The square is a unique geometric figure, due to the fact that it is certainly symmetrical, independently on how and where to draw the axis of symmetry.
Many people remember what a square is from school. This quadrilateral, which is regular, has absolutely equal angles and sides. Looking around, you can see that we are surrounded by many squares. Every day we come across them, and sometimes the need arises to find the area and perimeter of this geometric figure. Calculating these values is easy if you take a few minutes to watch this video tutorial explaining simple rules carrying out calculations.
Training video “How to find the area and perimeter of a square”
What do you need to know about the square?
Before you begin making calculations, you need to know some important information about this figure, including:
- all sides of the square are equal;
- all corners of a square are right;
- The area of a square is a way of calculating how much space a shape takes up in two-dimensional space;
- two-dimensional space is a sheet of paper or a computer screen where a square is drawn;
- the perimeter is not an indicator of the fullness of the figure, but allows you to work with its sides;
- perimeter is the sum of all sides of the square;
- When calculating the perimeter, we operate with one-dimensional space, which means recording the result in meters, not square meters (area).
How to find the area of a square?
Calculating the area of a given figure can be simply and easily explained using an example:
- Let's assume that the side of the square is 8 meters;
- to calculate the area of any rectangle, you need to multiply the value of one side by the other (8 x 8 = 64);
- since we multiply meters by meters, the result is square meters(m2).
How to find the perimeter of a square?
Knowing that all sides of a given rectangle are equal, you need to do the following manipulations to calculate its perimeter:
- add up all four sides of the square (8 + 8 + 8 + 8 = 32);
- the resulting value will be the perimeter of the square, recorded in meters.
All formulas and calculations given in this article are applicable for any rectangle. It is important to remember that when it comes to other rectangles that are not regular, the sides will have different values, for example 4 and 8 meters. This means that to find the area of such a rectangle, it will be necessary to multiply the sides of the figure that are different in value, and not the same ones.
It is also necessary to remember that the area is measured in square meters, and the perimeter in simple meters. If the perimeter is drawn as one long line, then its value will not change, which indicates that the calculations are carried out in one-dimensional space.
Area is measured in two dimensions, as indicated by square meters, which we get by multiplying meters by meters. Area is an indicator of the fullness of a geometric figure, and tells us how much imaginary coverage is needed to fill a square or other rectangle.
Simple explanations of the video lesson will allow you to quickly calculate the area and perimeter of not only a square, but also any rectangle. This knowledge from the school course will be useful when renovating a house or garden.
Square is a geometric figure that is a quadrilateral, all angles and sides of which are equal. It can also be called rectangle, whose adjacent sides are equal, or diamond, in which all angles are equal 90º. Thanks to absolute symmetry find square or perimeter of a square very easy.
Instructions:
- First, let's determine that perimeter is the sum of the lengths of all sides of a flat geometric figure, which is measured in the same quantities as the length. There are two ways to calculate the perimeter of a square.
Through side length and diagonal
- Because the perimeter of a square is determined by the sum of the lengths of all its sides, and the sides of a given figure are equal, then the value of this value can be calculated by multiplying the length of one side by the number “ 4 " Accordingly, the formulas will look like this: P = a + a + a + a or P = a * 4 , Where R- This perimeter of a square And A – side length.
- In addition, depending on the conditions of the problem, the perimeter of a square can be calculated by multiplying the length of its diagonal by two roots of two: P = 2√2 * d , Where R- This perimeter of a square And d- his diagonal.
- Some tasks require finding perimeter of a square knowing him square . This will also not be difficult to do. The area of a given figure is equal to the length of its side squared: S = a 2 , Where S – area of the square And A –length of its side. Or the area is equal to the square value of the length of its diagonal, divided by two: S = d 2 /2 , Where S- still the same square And d – diagonal of a square.
- Knowing the formulas and the value of the area, it is not difficult to find the length of the side or the length of the diagonal, and then return to the formulas for calculating the perimeter and calculate its value.
Through the radius of the inscribed and circumscribed circle
- Finally, it is important to understand and how to find perimeter of a square, if known circle radius described around it (or, on the contrary, inscribed in it). A circle inscribed in a given geometric figure touches the middle of each side, and its radius is equal to half of any side: R in = ½ a , Where R in – inscribed circle radius And A – side of a square.
- Circumcircle passes through all the vertices of the square and its radius is equal to half the length of the diagonal: R o = ½ d , Where R o – this radius of a circle circumscribed around a square And d- his diagonal.
- Therefore, in the first case, the perimeter will be calculated using the formula: Р = 8 R in , and in the second: P = 4 x √2 x R o .
Using websites and an online calculator
- If for some reason you suddenly forget the formulas, then the Internet will help you refresh your knowledge. Go to your browser, open the search engine page and enter the appropriate query in the window, for example: “ perimeter of a square formula" The system will display a huge number sites of a reference nature, which will help you in this matter, and will also allow you to cope with solving problems concerning other geometric shapes.
- In addition, if you do not want to understand formulas and calculate values yourself, then you can use the services Internet calculators . An example would be a website. Chapter " Formulas for the perimeter of geometric figures"contains theoretical information supported by visual illustrations. If you follow the link “ online calculator ", which is located in the window of each figure, then a page for calculations will open in front of you.
- Select in the window below on the basis of which you are going to calculate perimeter of a square(side or diagonal), and then enter the available data. The system will issue result , guided by established formulas.
- In addition, on the site you will find a lot of other information that can make it easier to work with math problems. If you wish, you can also look for more convenient or educational help sites.
- If you cannot figure out the process of solving the problem, then here you can turn to people who are good at solving mathematical exercises for help. They can always be found on the corresponding forums , for example, or.
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 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 is a numerical characteristic of a figure. Area measured square units lengths: 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 the 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.
