Area and perimeter of rectangles worksheets: Area and Perimeter of Rectangles Worksheets
Posted onArea and Perimeter Worksheets, Free Simple Printable Area and Perimeter Worksheets
Frequently Asked Questions
What can I learn from area and perimeter worksheets?
You can learn various concepts from the area and perimeter worksheets.
To begin the area and perimeter worksheets can help recapitulate the basic ideas and the definitions of area and perimeter. The area of any 2D shape is the amount of space occupied while the perimeter is defined as the sum of lengths for all the sides of the shape. While some of the area and perimeter worksheets focus on the methods of measuring area and perimeter are different from each other.
How can the area and perimeter worksheets help me with real life situations?
The concept of area and perimeter is integral for our daily life activities. If we have to describe the size of a house by the floor area or decide on the length of wire needed to fence off a field, then the concepts of ‘area’ and ‘perimeter’ are being utilized. With the help of area and perimeter worksheets, students will be able to connect with their surroundings and experience math outside the classroom.
Why should I take up area and perimeter worksheets?
The area and perimeter worksheets are ideal for students who want to consolidate their understanding of the concepts in a robust manner by attempting a wide variety of problems in a timed manner.
Will the the area and perimeter worksheets be helpful for 3D shapes?
BYJU’S Math has surface area worksheets for 3D shapes such as cones, prism, sphere, and cylinder as well.
Will the area and perimeter worksheets have sums based on the concept of surface area?
Yes, the area and perimeter worksheets have problem sums for the concept of surface area.
Surface Area is measured for three-dimensional shapes. Surface area of any 3D shape is defined as the sum total of the area of various faces a 3-D object may have. Understanding built around measuring area of 2-D shapes helps in mastering this concept as well.
What are the different kinds of area and perimeter worksheets prepared?
The area and perimeter worksheets are prepared with complete research with special focus on different concepts of the chapter. There are three levels for the worksheets – easy, medium and hard. The students can select any of the levels to work on the area and perimeter worksheets and once they are confident of their math skills, they can move to the next level.
Are the area and perimeter worksheets helpful?
The primary goal for the area and perimeter worksheets is to improve students’ understanding of the concepts while they solve the various types and levels of area and perimeter problems in an interesting way. The printable worksheet questions cover several sub-concepts of the area and perimeter chapter to ensure a comprehensive learning experience for the children.
Area and Perimeter of Rectangles from The Teacher’s Guide
Area and Perimeter
Area
Count the Square Units
Students count square units to
find the area of a rectangle.
Area
Skip Count the Square Units
Students Skip Count square units to
find the area of a rectangle.
Area
Muliply the Square Units
Students multiply the rows and
columns of square units to
find the area of a rectangle.
Area
Multiply the Side Lengths
Students multiply the side
lengths to
find the area of a rectangle.
Area
Multiply the Side Lengths 2
Students count square units to
find the area of a rectangle.
Area
Solve for Unknown Length or Width
Students solve for the unknown
length or width.
Area
of a Rectangle Distributive Property
Students use the distributive
property area model.
Area
Shaded Shapes
Students count square units to
find the area of a shaded shape.
Area
Make Two Rectangles
Students make a shape into two
rectangles to find the area.
Area
Count the Square Units
Students use grid cues to find the area of
the shaded shape.
Area
of Shaded Shape by Subtracting With Blocks
Students find the area of a shade
shape by making a full rectangle and subtracting.
Area
of Shaded Shape by Subtracting Without
Blocks
Students find the area of a shade
shape by making a full rectangle and subtracting.
Area
of Shaded Shape by Subtracting Copy
to Grid
Students find the area of a shade
shape copying the shape to a grid and counting the unit squares.
Perimeter
Counting Outer Edges
Students find perimeter of a
rectangle by counting the outer edges of outer square units.
Perimeter
Adding Outer Edges
Students find perimeter of a
rectangle by adding the outer edges of outer square units.
Perimeter
Adding Side Lengths
Students find the area of a shade
shape by making a full rectangle and subtracting.
Area
and Perimeter Side Lengths
Students find the area and
perimeter of a rectangle by working with side lengths.
Area
of and Perimeter Side Lengths 2
Students find the area and
perimeter of a rectangle by working with side lengths.
Area
and Perimeter Word Problems
Students solve word problems
involving area and perimeter.
Area
and Perimeter Word Problems
Students solve word problems
involving area and perimeter.
Area
and Perimeter Word Problems
Students solve word problems
involving area and perimeter.
Area
and Perimeter Dominoes
Students use dominoes to
calculate area.
Perimeter, area and volume
This material contains geometric figures with measurements. Measurements shown are approximate and may not match actual measurements.
The perimeter of a geometric figure
The perimeter of a geometric figure is the sum of all its sides. To calculate the perimeter, you need to measure each side and add the results of the measurements.
Calculate the perimeter of the following figure:
This is a rectangle. We will talk more about this figure later. Now just calculate the perimeter of this rectangle. Its length is 9cm and width 4 cm.
A rectangle has opposite sides equal. This is visible in the figure. If the length is 9 cm and the width is 4 cm, then the opposite sides will be 9 cm and 4 cm, respectively:
Let’s find the perimeter.
To do this, add all the sides. You can add them in any order, since the sum does not change from the rearrangement of the places of the terms. The perimeter is often indicated by the capital Latin letter P (eng. perimeters ). Then we get:
P = 9 cm + 4 cm + 9 cm + 4 cm = 26 cm
«repeat length and width twice»
P = 2 × (9 + 4) = 18 + 8 = 26 cm.
A square is the same rectangle, but with all sides equal. For example, let’s find the perimeter of a square with a side of 5 cm. The phrase «with a side of 5 cm» should be understood as «the length of each side of the square is 5 cm»
To calculate the perimeter, add all the sides:
P = 5 cm + 5 cm cm = 20 cm
But since all sides are equal, the calculation of the perimeter can be written as a product. The side of the square is 5 cm, and there are 4 such sides. Then this side, equal to 5 cm, must be repeated 4 times
P = 5 cm × 4 = 20 cm
Area of a geometric figure
Area of a geometric figure is a number that characterizes the size of this figure.
It should be clarified that in this case we are talking about the area on the plane. In geometry, a plane is any flat surface, for example: a sheet of paper, a plot of land, a table surface.
Area is measured in square units. Square units are squares whose sides are equal to one. For example, 1 square centimeter, 1 square meter or 1 square kilometer.
To measure the area of a figure means to find out how many square units are contained in this figure.
For example, the area of the following rectangle is three square centimeters:
This is because this rectangle contains three squares, each of which has a side equal to one centimeter: in this case is a square unit). If we look at how many times this square enters the rectangle presented on the left, we find that it enters it three times.
The following rectangle has an area of six square centimeters:
This is because this rectangle contains six squares, each of which has a side of one centimeter:
Let’s decide in which squares we will measure the area.
In this case, it is convenient to measure the area in square meters:
So, our task is to determine how many such squares with a side of 1 m are contained in the original room. Let’s fill the whole room with this square:
We see that a square meter is contained in a room 12 times. So the area of the room is 12 square meters.
Rectangle area
In the previous example, we calculated the area of the room by successively checking how many times it contains a square whose side is one meter. The area was 12 square meters.
The room was a rectangle. The area of a rectangle can be calculated by multiplying its length and width.
To calculate the area of a rectangle, you need to multiply its length and width.
Let’s go back to the previous example. Let’s say we measured the length of the room with a tape measure and it turned out that the length was 4 meters:
Now let’s measure the width.
Let it be 3 meters:
Multiply the length (4 m) by the width (3 m).
4 × 3 = 12
Like last time, we get twelve square meters. This is explained by the fact that by measuring the length, we thereby find out how many times it is possible to fit a square with a side equal to one meter in this length. We lay four squares in this length:
We then determine how many times this length can be repeated with the squares stacked. We find this out by measuring the width of the rectangle:
Square area
A square is the same rectangle, but with all sides equal. For example, the following figure shows a square with a side of 3 cm. The phrase «a square with a side of 3 cm» means that all sides are 3 cm to the width.
Calculate the area of a square with a side of 3 cm. Multiply the length of 3 cm by the width of 3 cm
3 × 3 = 9
In this case, it was required to find out how many squares with a side of 1 cm are contained in the original square.
The original square contains nine squares with a side of 1 cm. Indeed, it is so. A square with a side of 1 cm enters the original square nine times:
Multiplying the length by the width, we get the expression 3 × 3, and this is the product of two identical factors, each of which is 3. In other words, the expression 3 × 3 represents is the second power of the number 3. So the process of calculating the area of a square can be written as a power of 3 2 .
Therefore, the second power of the number is called the square of the number . When calculating the second power of the number a , a person thereby finds the area of a square with a side of a . The operation of raising a number to the second power is otherwise called squaring .
Designations
The area is designated by the capital Latin letter S . Then the area of a square with side a cm will be calculated according to the following rule
S = a 2
where a is the length of the side of the square.
The second degree indicates that two identical factors are multiplied, namely the length and width. It was previously said that all sides of a square are equal, which means that the length and width of the square, expressed through the letter a , are equal.
If the task is to determine how many squares with a side of 1 cm are contained in the original square, then cm should be indicated as units of measurement for the area 2 . This designation replaces the phrase «square centimeter» .
For example, we calculate the area of a square with a side of 2 cm.
So a square with a side of 2 cm has an area equal to four square centimeters: contained in the original square, then m 2 should be indicated as units of measurement. This designation replaces the phrase «square meter» .
Calculate the area of a square with a side of 3 meters
Hence, a square with a side of 3 m has an area equal to nine square meters:
Similar notation is used when calculating the area of a rectangle.
But the length and width of the rectangle can be different, so they are denoted by different letters, for example a and b . Then the area of a rectangle with length a and width b is calculated according to the following rule:
S = a × b
As in the case of a square, the units for the area of a rectangle can be cm 2 , m 2 , km 2 . These designations replace the phrases «square centimeter», «square meter», «square kilometer» , respectively.
For example, let’s calculate the area of a rectangle 6 cm long and 3 cm wide
So a rectangle 6 cm long and 3 cm wide has an area equal to eighteen square centimeters:
The phrase “square units” can be used as a unit of measure. For example, the entry S \u003d 3 square units means that the area of a square or rectangle is equal to three squares, each of which has a unit side (1 cm, 1 m or 1 km).
Area units conversion
Area units can be converted from one unit of measure to another. Consider a few examples:
Example 1 . Express 1 square meter in square centimeters.
1 square meter is a square with a side of 1 m. That is, all four sides have a length of one meter.
But 1 m = 100 cm. Then all four sides also have a length equal to 100 cm
Calculate the new area of this square. Multiply the length of 100 cm by the width of 100 cm or square the number 100
S = 100 2 = 10,000 cm 2
It turns out that there are ten thousand square centimeters per square meter.
1 m 2 = 10,000 cm 2
This allows you to multiply any number of square meters by 10,000 in the future to get the area expressed in square centimeters.
To convert square meters to square centimeters, multiply the number of square meters by 10,000.
And to convert square centimeters to square meters, you need to divide the number of square centimeters by 10,000.
For example, let’s convert 100,000 cm 2 to square meters. In this case, it is possible to reason like this: “ if 10 000 cm 2 is one square meter, then how many times 100,000 cm 2 will contain 10 000 cm 2 ”
9000 100 000 cm 2 : 10,000 cm 2 = 10 m 2
Other units can be converted in the same way. For example, let’s convert 2 km 2 to square meters.
One square kilometer is a square with a side of 1 km. That is, all four sides have a length equal to one kilometer. But 1 km \u003d 1000 m. So, all four sides of the square are also equal to 1000 m. Let’s find the new area of the square, expressed in square meters. To do this, multiply the length of 1000 m by the width of 1000 m or square the number 1000
S = 1000 2 = 1 000 000 m 2
It turns out that there is one million square meters per square kilometer:
1 km 2 = 1,000,000 m 2
This allows you to multiply any number of square kilometers by 1,000,000 in the future to get an area expressed in square meters.
To convert square kilometers to square meters, you need to multiply the number of square kilometers by 1,000,000.
So, back to our problem. It was required to convert 2 km 2 into square meters. Multiply 2 km 2 by 1,000,000
2 km 2 × 1,000,000 = 2,000,000 m 2
2 to square kilometers. In this case, you can reason like this: “ if 1,000,000 m 2 is one square kilometer, then how many times 3,500,000 m 2 will each contain 1,000,000 m 2 »
3,500,000 m 2 : 1,000,000 m Express 7 m 2 in square centimeters.
Multiples 7 m 2 by 10 000
7 m 2 = 7 m 2 × 10 000 = 70 000 cm 2
Example 3 . Express 5 m 2 13 cm 2 in square centimeters.
5 m 2 13 cm 2 = 5 m 2 × 10,000 + 13 cm 2 = 50,013 cm Express 550,000 cm 2 in square meters.
Find out how many times 550,000 cm 2 contains 10,000 cm 2 . To do this, we divide 550 000 cm 2 by 10,000 cm 2
550 000 cm 2 : 10,000 cm 2 = 55 m 2
9000 Example 5 . Express 7 km 2 in square meters.
Multiples 7 km 2 by 1,000,000,000
7 km 2 × 1,000 000 = 7,000,000 m 2
Example 6 . Express 8,500,000 m 2 in square kilometers.
Find out how many times 8,500,000 m 2 contains 1,000,000 m 2 each. To do this, we divide 8,500,000 m 2 by 1,000,000 m 2
8,500,000 m 2 × 1,000,000 m 2 = 8.5 km 2
Land area units
It is convenient to measure the area of small land plots in square meters.
Larger plots are measured in ares and hectares.
Ar (abbreviated: a ) is an area equal to one hundred square meters (100 m 2 ). In view of the frequent distribution of such an area (100 m 2 ), it began to be used as a separate unit of measurement.
For example, if it is said that the area of a field is 3 a, then you need to understand that these are three squares with an area of 100 m 2 each, that is:
3 a = 100 m 2 × 3 = 300 m 2
People often call ar weave , since ar is equal to a square with an area of 100 m 2 . Examples:
1 weave = 100 m 2
2 weave = 200 m 2
10 weave = 1000 m 2
A hectare (abbreviated: ha) is an area equal to 10,000 m 2 . For example, if it is said that the area of a forest is 20 hectares, then you need to understand that these are twenty squares of 10,000 m2 2 each, that is:
20 hectares = 10,000 m m 2
Rectangular box and cube
Rectangular box is a geometric figure consisting of faces, edges and vertices.
The figure shows a rectangular box:
Yellow color shows faces of the parallelepiped, black color shows edges , red color shows vertices .
A cuboid has a length, width and height. The figure shows where the length, width and height are:
A parallelepiped whose length, width and height are equal to each other is called cube . The figure shows a cube:
The volume of the geometric figure
The volume of a geometric figure is a number that characterizes the capacity of this figure.
Volume is measured in cubic units. Cubic units mean cubes with a length of 1, a width of 1 and a height of 1. For example, 1 cubic centimeter or 1 cubic meter.
To measure the volume of a figure means to find out how many cubic units fit in this figure.
For example, the volume of the following cuboid is twelve cubic centimeters:
This is because this parallelepiped contains twelve cubes 1 cm long, 1 cm wide and 1 cm high:
One of the units for measuring volume is the cubic centimeter (see 3 ).
Then the volume V of the parallelepiped we have considered is 12 cm 3
V = 12 cm 3
The volume of a cuboid is equal to the product of its length, width and height .
V = ABC
Where, A — length, b — width, C
So, in the previous example, we visually determined that the volume of the parallelepiped is 12 cm 3 . But you can measure the length, width and height of a given box and multiply the measurement results. We will get the same result
The volume of the cube is calculated in the same way as the volume of the cuboid — multiply the length, width and height.
For example, let’s calculate the volume of a cube, the length of which is 3 cm. The cube has the same length, width and height. If the length is 3 cm, then the width and height of the cube are equal to the same three centimeters:
We multiply the length, width, height and get a volume equal to twenty-seven cubic centimeters:
V = 3 × 3 × 3 = 27 cm³
Indeed, the original cube contains 27 cubes 1 cm long
When calculating the volume of this cube, we multiplied the length, width and height.
The product is 3 × 3 × 3. This is the product of three factors, each of which is equal to 3. In other words, the product of 3 × 3 × 3 is the third power of 3 and can be written as 3 3 .
V = 3 3 = 27 cm 3
Therefore, the third power of a number is called the cube of the number . When calculating the third power of the number a , a person thereby finds the volume of a cube, with a length of a . The operation of raising a number to the third power is otherwise called cubed .
Thus, the volume of a cube is calculated according to the following rule:
V = a 3
Where a is the length of the cube.
Cubic decimeter. Cubic meter
It is not convenient to measure all objects of our world in cubic centimeters. For example, it is more convenient to measure the volume of a room or house in cubic meters (m 3 ).
And the volume of a tank, aquarium or refrigerator is more convenient to measure in cubic decimeters (dm 3 ).
Another name for one cubic decimeter is one liter.
1 dm 3 = 1 liter
Volume unit conversion
Volume units can be converted from one unit of measure to another. Consider a few examples:
Example 1 . Express 1 cubic meter in cubic centimeters.
One cubic meter is a cube with a side of 1 m. The length, width and height of this cube are equal to one meter.
But 1 m = 100 cm. Hence, the length, width and height are also equal to 100 cm
Let’s calculate the new volume of the cube, expressed in cubic centimeters. To do this, multiply its length, width and height. Or let’s raise the number 100 to a cube:
V = 100 3 = 1,000,000 cm 3
It turns out that there are one million cubic centimeters per cubic meter:
1 m 3 = 1,000,000 cm volume expressed in cubic centimeters.
To convert cubic meters to cubic centimeters, multiply the number of cubic meters by 1,000,000.
And to convert cubic centimeters to cubic meters, you need to divide the number of cubic centimeters by 1,000,000.0007
For example, let’s convert 300,000,000 cm 3 to cubic meters. In this case, it is possible to reason like this: “ if 1,000 000 cm 3 is one cubic meter, then how many times ,300,000,000 cm 3 will contain 1,000,000 cm 3 ”
” 300,000,000 cm 3 : 1,000,000 cm 3 = 300 m 3
Example 2 . Express 3 m 3 in cubic centimeters.
Multiply 3 m 3 by 1,000,000
3 m 3 × 1,000,000 = 3,000,000 cm 3
901 Express 60,000,000 cm 3 in cubic meters.
Find out how many times 60,000,000 cm 3 contains 1,000,000 cm 3 .
To do this, we divide 60,000,000 cm 3 by 1,000,000 cm 3
60,000,000 cm 3 : 1,000,000 cm 3 9015 5 7 = 65 m0007
The capacity of a tank, can or canister is measured in liters. A liter is also a unit of volume. One liter is equal to one cubic decimeter.
1 liter = 1 dm. When solving some problems, it may be useful to be able to convert liters to cubic decimeters and vice versa. Let’s look at a few examples.
Example 1 . Convert 5 liters to cubic decimetres.
To convert 5 liters to cubic decimeters, just multiply 5 by 1
5 liters × 1 = 5 dm 3
Example 2 Convert 6000 liters to cubic meters.
Six thousand liters is six thousand cubic decimeters:
6000 l × 1 = 6000 dm 3
Length, width and height of one cubic meter are equal to 10 dm
If you calculate the volume of this cube in decimeters, we get 1000 DM 3
V = 10 3 = 1000 DM 3
It turns out that one thousand cubic decimeters corresponds to one cubic meter.
And to determine how many cubic meters correspond to six thousand ml of cubic decimeters, you need to find out how many times 6,000 dm 3 contains 1,000 dm 3
6,000 dm 3 : 1,000 dm 3 = 6 m 3
So 6000 l = 6 m
Table of squares
In life, you often have to find the areas of various squares. To do this, each time you need to raise the original number to the second power.
The squares of the first 99 natural numbers have already been calculated and entered in a special table called the table of squares .
The first row of this table (numbers from 0 to 9) are units of the original number, and the first column (numbers from 1 to 9) is the tens of the original number.
For example, let’s find the square of the number 24 in this table. The number 24 consists of the numbers 2 and 4. More precisely, the number 24 consists of two tens and four ones.
So, select the number 2 in the first column of the table (the tens column), and select the number 4 in the first row (the units row). Then, moving to the right of the number 2 and down from the number 4, we find the intersection point. As a result, we will find ourselves in the position where the number 576 is located. So, the square of the number 24 is the number 576
24 2 = 576
Table of cubes
As in the case of squares, the cubes of the first 99 natural numbers have already been calculated and entered in a table called
1 table2 of cubes.
The cube of a number according to the table is determined in the same way as the square of a number. For example, let’s find the cube of the number 35. This number consists of the numbers 3 and 5. We select the number 3 in the first column of the table (the tens column), and we select the number 5 in the first row (the line of units). Moving to the right of the number 3 and down from the number 5, we find the intersection point.
As a result, we will find ourselves in the position where the number 42875 is located. Therefore, the cube of the number 35 is the number 42875.
35 3 = 42875
Problems for independent solution
Problem 1. The length of the rectangle is 6 cm and the width is 2 cm. Find the perimeter.
Decision
P = 2 ( A + B )
A = 6, b = 2
P = 2 (6 + 2) = 12 + 4 = 16 cm
Answer: the perimeter of the rectangle is 16 cm.
Show solution
Problem 2. The length of the rectangle is 6 cm and the width is 2 cm. Find the area.
Decision
S = AB
A = 6, b = 2
S = 12 cm 2
Square: The area is 12 cm 2 .
Show solution
Problem 3. The area of a rectangle is 12 cm 2 .
The length is 6 cm. Find the width of the rectangle.
6 Decision
S = AB
= 12, A = 6, B = x
12 = 6 × x
x
000 Reply: Shine width: Shine widering The rectangle is 2 cm.
show the solution
Task 4. Calculate the area of the square with a side of 8 cm
Decision
S = A 2
A
S = 8 2 2 = 64 cm 2
Answer: the area of a square with a side of 8 cm is 64 cm 2
Show the solution
.
Decision
V = ABC
A = 6, B = 4, C
V = 6 × 4 × 3 = 72 cm 3 .
Answer: the volume of a rectangular parallelepiped whose length is 6 cm, width 4 cm, height 3 cm is equal to 72 cm 3
Show solution
Problem 6.
The volume of a cuboid is 200 cm 3 . Find the height of the box if its length is 10 cm and its width is 5 cm
200 = 10 × 5 × x
200 = 50 x
x = 4
0007
Show solution
Problem 7. The areas of land sown with wheat and flax are proportional to the numbers 4 and 5. On what area is wheat sown if 15 hectares are sown under flax
Solution
. And the number 5 reflects the area sown with flax.
It is said that the areas sown with wheat and flax are proportional to these numbers.
Simply put, how many times the numbers 4 or 5 change, how many times the area sown with wheat or flax will change. 15 hectares were sown with flax. That is, the number 5, which reflects the area sown with flax, has changed 3 times.
Then the number 4, which reflects the area sown with wheat, must be tripled
4 × 3 = 12 hectares
Answer: 12 hectares were sown with wheat.
Show solution
Problem 8. The length of the granary is 42 m, the width is the length, and the height is 0.1 length. Determine how many tons of grain the granary holds if 1 m 3 weighs 740 kg.
Solution
a — length
b — width
c — height
A = 42 m
b = m
c = 42 × 0.1 = 4.2 m
Determine the volume of the granarium:
v = ABC 2020 = 42 × 30 × 4.2 = 5292 m 3
Determine how many tons of grain the granaries contains:
5292 × 740 = 3916080 kg
We will transfer kilograms to tons:
Answer: COMPLEMENTS: Grainstorm 08 tons of grain.
Show solution
Problem 9. 12. The pool has the shape of a rectangular parallelepiped, the length of which is 5.8 m and the width is 3.5 m. 25 l / min is poured into them, and through the second — 0.
75 of this amount. Determine the height (depth) of the pool.
Solution
Determine how many liters per minute are poured into the pool through the second pipe:
25 l/min × 0.75 = 18.75 l/min
Determine how many liters per minute are poured into the pool through both pipes:
25 l/min + 18.75 l/min = 43.75 l/min 812 min = 35,525 l
1 l = 1 dm 3
35,525 l = 35,525 dm 3
Convert to cubic decimeters. This will calculate the volume of the pool:
35 525 dm 3 : 1000 dm 3 = 35.525 m 3
Knowing the volume of the pool, you can calculate the height of the pool. Substitute in the letter equation V=abc the values we have. Then we get:
V = 35.525
A = 5.8
b = 3.5
C x
35.525 = 5.8 × x
35.525 = 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20.
3 × x
x = 1.75 m
s = 1.75
Answer: the height (depth) of the pool is 1.75 m.
Show solution
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Posted Author
Difficulties in learning the concepts of «perimeter» and «area» in elementary school
Author :
Nagimova Maria Khaydarovna
Category : 5. Pedagogy of the comprehensive school
Published in
XXII International Scientific Conference «Pedagogical Mastery» (Kazan, February 2022)
Date of publication : 30.01.
2022
66
Article viewed:
317 times
Download electronic version
References:
Nagimova, M. Kh. Difficulties in studying the concepts of «perimeter» and «area» in elementary school / M. Kh. Nagimova. — Text: direct // Pedagogical excellence: materials of the XXII Intern. scientific conf. (Kazan, February 2022). — Kazan: Young scientist, 2022. — S. 37-40. — URL: https://moluch.ru/conf/ped/archive/417/16937/ (date of access: 10/25/2022).
Why do children confuse the concepts of «perimeter» and «area»? In elementary school mathematics, the concept of perimeter is studied much earlier than area. Children gradually learn to find the sum of the lengths of the sides of a polygon, the skill gradually comes to automatism. When finding the perimeter of a rectangle in several ways, everything also goes smoothly.
But suddenly … it’s time to study the topic «Square of Figures», and then the students begin to get confused. What can be done to avoid confusion between these concepts?
When studying the topic «Perimeter» it is necessary to increase the number of practical tasks. Students will learn the material best when they themselves walk around the school site with a tape measure and measure the perimeter of the gazebo, sports ground, office, library, corridor, etc. It is important that children find the perimeter in different units of length.
Before studying the topic «Area», you need to include tasks for finding the perimeter in each lesson.
In the first lessons of studying the concept of “Area of geometric shapes”, it is necessary to alternate tasks for finding the perimeter and area.
For more solid assimilation, you can use the game of color in the lessons. Write the formulas for finding the perimeter in green, and the area in red. If you constantly focus on color designation, students get used to the algorithm and quickly navigate in choosing a formula for completing tasks.
Inverse problems should also be included in the work with finding the perimeter. For example, 1) From a wire 9 cm long, different triangles. How long (in centimeters) can the sides of the triangle be? Is it possible to consider the lengths of all sides of the wire as a perimeter? Before studying the topic “Area”, give the following task: 2) Brother and sister found the perimeter of five different rectangles and got 24 cm. What sizes could these rectangles have? Draw these rectangles. It is necessary to complete this task on leaflets, and then, when the children learn how to find the area of \u200b\u200bthe rectangle, you need to return to this task and already find the area of the same rectangles.
Of course, not all teaching staff will be able to give such tasks. For example, according to the textbook by I. I. Arginskaya (L. V. Zankov’s system), the section “Area and its measurement” is at the very beginning of the textbook for grade 3. Naturally, here it is impossible to start studying the topic by repeating the topic of finding the perimeter of a rectangle.
The algorithm will methodically be the same as in working with any other value, but here it is already possible to make a comparison, because there are figures that have one-dimensionality (through the exercise). Using visual material, we consider the concept of «Square», where we met with this in life. With the help of tasks, we work out, isolate, classify positions, use different measures, compare which of them are convenient and which are inconvenient. Next, we direct the children to the fact that it is necessary to use some kind of identical measurements, because different measurements do not give the correct picture of comparing the areas of rectangles with different sizes. In practice, in one of the tasks it is proposed to draw rectangles on paper, cut them out and try to put them on top of each other. The winning position here will be played by completing the task on paper in a cage. It is clear that the cell can serve as a measure for measuring the area. In the following lessons, gradually a measure of one cell size displaces all other measurements.
Here it is important to bring the children to the fact that in geometry there is no unit of length — 1 cell, but there is a unit of length — 1 centimeter, and it is a square with a side of 1 centimeter that can be an ideal measure for calculating the area of a rectangle. The following is a formula for finding the area of a rectangle.
It is useful to perform such an exercise for comparing areas. The teacher hangs out two rectangles of different colors, but the same size, One of them is divided into 8 equal squares, and the other into 32 of the same squares. The teacher asks the children to first count how many squares the first rectangle is divided into. Record the score on the board. Similar work is carried out with another rectangle. Then, according to the number of squares found, the children compare the areas of the rectangles. As a rule, children make erroneous conclusions. But the wrong conclusion leads to an understanding of the need for new units for measuring the areas of geometric shapes.
Linear units are not suitable for measuring area; new units are needed — area units.
One of the effective tasks for showing the difference between the concepts of perimeter and area is a practical task for constructing a rectangle from wire and cardboard:
1) Bend the wire into a rectangular shape 8 cm long and 5 cm wide.
2) From cardboard cut out a rectangle 8 cm long and 5 cm wide.
3) Compare the wire figure with the cardboard figure. What can you say? (at this stage, children can answer that they have the same size and shape)
4) Find the perimeter of the wire figure (children find the perimeter of the rectangle in any way).
5) Is it possible to unbend a wire figure into a line? (children see that the figure came out “empty”, it is not flat and it is easy to straighten it). Is it possible to do the same with a cardboard figure? Why?
6) Can we say that the perimeter of the rectangle and the length of the line are equal? Why?
7) Are the perimeters of these figures equal? Why?
This task must be given to kinesthetic learners.
