Before solving problems of finding the perimeter and area of geometric figures, let me remind you that...
I level
1. The length of the rectangle is 8 dm, width is 7 dm. Find its area.
2.The length of the side of the square is 6 cm. Find out the area and perimeter of the square.
3. A rectangle has a length of 7 cm and a width of 5 cm. Find out the area and perimeter of the rectangle.
4.Find the perimeter and area of a rectangle with sides 6 cm and 8 cm.
5. The length of the rectangle is 8 dm, width is 5 dm. Find its area.
6.Calculate the area of a rectangle whose side lengths are 6 mm and 8 mm.
7. The width of the rectangle is 7 dm, and the length is 12 dm. Calculate the area.
8. The length of the rectangle is 9 dm, width is 7 cm. Find its area.
9.The length of the side of the square is 6 cm. Find out the area.
10.Calculate the perimeter of a square with a side of 4 cm.
11. The width of the rectangle is 9 dm, and the length is 6 dm more. Find its area.
12. The length of the rectangle is 5 dm, the width is 4 cm less. Find the P and S of this rectangle.
13.Draw a rectangle, the length of one side of which is 2 cm, and the length of the other is 3 times greater. Find its perimeter and area.
14.Draw a rectangle, the length of one side of which is 6 cm, and the length of the other is 2 times greater. Find its perimeter and area.
15.Draw a rectangle whose width is 2 cm and whose length is 3 cm more. Calculate its perimeter.
16. The side of a square is 3 cm. What is the perimeter?
17. A sheet of paper has a square shape. Its side is 10 cm. What is the perimeter?
18.Draw a square with a side of 6 cm. Find its perimeter. The perimeter of the square is 28 cm. What is its side?
19. The width of a rectangular window is 4 dm, and the length is 2 times greater. Calculate the area of the window.
20. The width of the rectangle is 4 dm, and the length is 5 times the width. Find the area of the rectangle.
21. The area of the rectangle is 36 cm², its length is 9 cm. What is the width of the rectangle?
Level II
1.Draw a rectangle, the length of one side of which is 2 cm, and the length of the other is 4 times greater. Find its perimeter and area.
2. The length of the rectangle is 5 dm, the width is 4 cm less. Find the P and S of this rectangle.
3. Given: a rectangle, a = 8 dm, c - 2 cm less. Find P and S.
4. The length of the rectangle is 12 cm, and its width is 2 cm less. Find the area and perimeter of the rectangle.
5. The sum of the two sides of the square is 12 dm. Find the perimeter and area of the square.
6. Find the length of the rectangle based on its width - 8 dm and perimeter - 30 dm.
7. The perimeter of a square is 32 cm. What is its side?
8. The perimeter of the triangle is 21 cm. Find the length of the third side of this triangle if the lengths of the two sides are 7 cm and 8 cm.
9. The perimeter of the rectangle is 20 cm. The length of its side is 6 cm. Find out the width of the rectangle and draw it.
10. The area of the rectangle is 270 sq. cm, its length is 9 dm. Find the perimeter of this rectangle.
11.Perimeter rectangle is 54 m. Find the area of this rectangle if one side is 18 m.
12. Find the area of a square whose perimeter is 360 mm.
13. The perimeter of the rectangle is 40 cm. One side is 5 cm. What is its area?
14. Draw a square whose perimeter is equal to the perimeter of a rectangle with sides 2 cm and 6 cm.
15. A rectangular dacha plot has a length of 20 m and a width of 12 m. How long should a fence be placed around the plot?
16. The perimeter of a square is equal to the perimeter of a triangle with sides 6 cm, 3 cm and 7 cm. What is the length of the side of the square?
17. Which figure has a larger area and by how much: a square with a side of 4 cm or a rectangle with sides of 2 cm and 6 cm?
18. The perimeter of the rectangle is 54 m. Find the area of this rectangle if one side is 18 m.
19. The perimeter of a square sandbox is 12 m. Find the area of this sandbox.
20. Write all possible lengths and widths of the rectangle if its perimeter is 24 cm.
Compiled by Lyudmila Borisovna K islova
Additional materials
Dear users, do not forget to leave your comments, reviews, wishes. All materials have been checked by an anti-virus program.
Teaching aids and simulators in the Integral online store for grade 3
Trainer for 3rd grade "Rules and exercises in mathematics"
Electronic textbook for grade 3 "Math in 10 minutes"
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 is measured in square units of length: cm 2, m 2, dm 2, etc. (centimeter squared, meter squared, decimeter squared, etc.)In calculations it is denoted by a Latin letter S.
To determine the area of a rectangle, multiply the length of the rectangle by its width. 
The area of the rectangle is calculated by multiplying the length of the AC by the width of the CM. Let's write this down as a formula.
S AKMO = AK * KM
Example.
What is the area of rectangle AKMO if its sides are 7 cm and 2 cm?
S AKMO = AK * KM = 7 cm * 2 cm = 14 cm 2.
Answer: 14 cm 2.
Formula for calculating the area of a square
The area of a square can be determined by multiplying the side by itself.Example. 
In this example, the area of 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.
Subscribe to the site
Guys, we put our soul into the site. Thank you for that
that you are discovering this beauty. Thanks for the inspiration and goosebumps.
Join us on Facebook And In contact with
Perimeter is a geometric term that often appears in problems. To understand what a perimeter is, you should draw an arbitrary polygon and arm yourself with a ruler. Translated from Greek, this term means “I measure around.”
How to calculate perimeter
The perimeter is indicated by a Latin letter P. It can be measured in centimeters, millimeters, meters or decimeters. To find the perimeter, measure the length of all sides of the polygon. The resulting values must be added. The final sum will be the answer to the question: “What is the perimeter of the polygon?”
Perimeter is the length of the lines that limit a closed figure (square, rectangle, triangle, etc.).
For example, in front of you is a polygon with sides of 10, 12, 13 and 11 cm. We add the above numbers (10+12+13+11) and get the sum 46. This is the perimeter of the polygon.
For the convenience of calculating the perimeter in geometry, there are a number of formulas. Each formula corresponds to a specific figure.
Perimeter and area of a square
This is the sum of its four sides. As we know, all sides of a square are equal in size. Therefore, we can find out the perimeter of a square by multiplying its side length by four:
P= a+a+a+a
For example, we have a square with a side of 10 cm.
Answer: 40 cm
P= 10+10+10+10
P=40
Answer: 40 cm
To understand what perimeter and area are, you should understand that perimeter calculates the length of the contour of a figure, and area is the size of its entire surface.
To find out the area of a square, you need to use a simple formula:
S is the area, and is the side of the square.
For example, the problem states that the length of the side of the square is 10 cm.
S= 100cm 2
Answer: 100 cm 2
Perimeter and area of a rectangle
The sides of a rectangle that are opposite each other and have the same length are called opposite. These are length and width, they are conventionally designated by the Latin letters a and b. The formula for calculating the perimeter of a rectangle looks like this:
P= (a+b)*2
Using this formula, we first find the sum of the width and length and then multiply it by two.
For example, we have a rectangle with a length of 6 cm and a width of 2 cm.
P= (6+2) * 2
P= 16
Answer: 16 cm
To find out the area of a rectangle, multiply the length by the width. The formula looks like this:
For example, the task conditions say that the rectangle has a length of 5 cm and a width of 2 cm. We change the letters a and b to the indicated numbers.
S= 5*2
S=10cm 2
Answer: 10 cm 2
Perimeter of a circle (circumference)
Each circle has a center. The distance from the center of the circle to any point located on the circle is called the radius of the circle. Often students confuse the concepts of “circle” and “circle” and try to determine the area of a circle. This is a serious mistake. You should separate the concepts of “circle” and “circle” in your head. A circle does not and cannot have area, it only has length.
To find the perimeter of a circle, you need to calculate its circumference. There is a formula for finding the circumference of a circle:
L = 2πr
L- circumference
π is the number “pi”, a mathematical constant. It is equal to the ratio of the circumference of a circle to the length of its diameter. The ancient name for the number "pi" is Ludolph's number. This number is irrational; its decimal representation after the dot never ends.
π = 3.141 592 653 589 793 238 462 643 383 279 502
For ease of calculation, the value 3.14 is usually used
R is the radius of the circle
D– Circle diameter
So, to determine the perimeter of a circle, we need to find the product of the radius and 2π. If the problem specifies a diameter, then
For example, in front of us is a circle with a radius of 3 cm. Let’s find its perimeter.
L= 2*3,14*3
L=6 π
L=6*3.14
L= 18.84 cm
PTo= 18.84 cm
Answer: 18.84 cm
The difference between perimeter and area
Area is the size of the surface of a figure, and perimeter is the sum of its boundaries.
Area is always measured in square units (cm 2, m 2, mm 2). The perimeter is measured in units of length - centimeters, millimeters, meters, decimeters.
Etc.:
If you look closely at all these figures, you can identify 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: an internal and external area relative to the figure to which it belongs:
Perimeter
The perimeter is the closed boundary of a flat geometric figure, separating its internal region from the external 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 called the length.
The perimeter is measured in length units: mm, cm, dm, m, km.
For all polygons, finding the perimeter comes down 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, perimeter is often denoted by the capital 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 figures is the internal region, that is, that part of the plane that is inside the perimeter.
Measure area figures - means finding how many times another figure, taken as a unit of measurement, is placed in a given figure. Typically, the unit of area is taken to be a square, the side of which is equal to the unit 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 units of length. Area units include: mm 2, cm 2, m 2, km 2, etc.
Square conversion table
| mm 2 | cm 2 | dm 2 | m 2 | ar (weave) | hectare (ha) | km 2 | |
|---|---|---|---|---|---|---|---|
| mm 2 | 1 mm 2 | 0.01 cm 2 | 10 -4 dm 2 | 10 -6 m 2 | 10 -8 are | 10 -10 ha | 10 -12 km 2 |
| cm 2 | 100 mm 2 | 1 cm 2 | 0.01 dm 2 | 10 -4 m 2 | 10 -6 are | 10 -8 ha | 10 -10 km 2 |
| dm 2 | 10 4 mm 2 | 100 cm 2 | 1 dm 2 | 0.01 m2 | 10 -4 are | 10 -6 ha | 10 -8 km 2 |
| m 2 | 10 6 mm 2 | 10 4 cm 2 | 100 dm 2 | 1 m2 | 0.01 are | 10 -4 ha | 10 -6 km 2 |
| ar | 10 8 mm 2 | 10 6 cm 2 | 10 4 dm 2 | 100 m 2 | 1 are | 0.01 ha | 10 -4 km 2 |
| ha | 10 10 mm 2 | 10 8 cm 2 | 10 6 dm 2 | 10 4 m 2 | 100 are | 1 ha | 0.01 km 2 |
| km 2 | 10 12 mm 2 | 10 10 cm 2 | 10 8 dm 2 | 10 6 m 2 | 10 4 ar | 100 ha | 1 km 2 |
| 10 4 = 10 000 | 10 -4 = 0,000 1 |
| 10 6 = 1 000 000 | 10 -6 = 0,000 001 |
| 10 8 = 100 000 000 | 10 -8 = 0,000 000 01 |
| 10 10 = 10 000 000 000 | 10 -10 = 0,000 000 000 1 |
| 10 12 = 1 000 000 000 000 | 10 -12 = 0,000 000 000 001 |
One of the basic concepts of mathematics is the perimeter of a rectangle. There are many problems on this topic, the solution of which cannot be done without the perimeter formula and the skills to calculate it.
Basic Concepts
A rectangle is a quadrilateral in which all the angles are right and the opposite sides are equal and parallel in pairs. In our life, many figures have the shape of a rectangle, for example, the surface of a table, a notebook, etc.
Let's look at an example: A fence must be erected along the boundaries of the land plot. In order to find out the length of each side, you need to measure them.
Rice. 1. A plot of land in the shape of a rectangle.
The plot of land has sides with lengths of 2 m, 4 m, 2 m, 4 m. Therefore, to find out the total length of the fence, you need to add up the lengths of all sides:
2+2+4+4= 2·2+4·2 =(2+4)·2 =12 m.
It is this quantity that is generally called the perimeter. Thus, to find the perimeter, you need to add up all the sides of the figure. The letter P is used to denote the perimeter.
To calculate the perimeter of a rectangular figure, you do not need to divide it into rectangles; you only need to measure all sides of this figure with a ruler (tape measure) and find their sum.
The perimeter of a rectangle is measured in mm, cm, m, km and so on. If necessary, the data in the task is converted into the same measurement system.
The perimeter of a rectangle is measured in various units: mm, cm, m, km and so on. If necessary, the data in the task is converted into one measurement system.
Formula for the perimeter of a figure
If we take into account the fact that the opposite sides of a rectangle are equal, then we can derive the formula for the perimeter of a rectangle:
$P = (a+b) * 2$, where a, b are the sides of the figure.
Rice. 2. Rectangle, with opposite sides marked.
There is another way to find the perimeter. If the task is given only one side and the area of the figure, you can use to express the other side in terms of the area. Then the formula will look like this:
$P = ((2S + 2a2)\over(a))$, where S is the area of the rectangle.
Rice. 3. Rectangle with sides a, b.
Exercise : Calculate the perimeter of a rectangle if its sides are 4 cm and 6 cm.
Solution:
We use the formula $P = (a+b)*2$
$P = (4+6)*2=20 cm$
Thus, the perimeter of the figure is $P = 20 cm$.
Since the perimeter is the sum of all sides of a figure, the semi-perimeter is the sum of only one length and width. To get the perimeter, you need to multiply the semi-perimeter by 2.
Area and perimeter are two basic concepts for measuring any figure. They should not be confused, although they are related. If you increase or decrease the area, then, accordingly, its perimeter will increase or decrease.
