Area and perimeter of rectangle worksheet: Area and Perimeter of Rectangle

Posted on 10 сентября, 2023 by alexxlab

50+ Perimeter of a Rectangle worksheets for 4th Year on Quizizz

Perimeter of a Rectangle: Discover a collection of free printable math worksheets for Year 4 students, focusing on calculating the perimeter of rectangles. Enhance learning and explore new strategies with Quizizz.

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Explore printable Perimeter of a Rectangle worksheets for 4th Year

Perimeter of a Rectangle worksheets for Year 4 are an essential resource for teachers looking to help their students master the concept of perimeter in Math. These worksheets focus on the fundamental principles of Geometry, specifically the calculation of the perimeter of a rectangle. By incorporating a variety of problems and exercises, these worksheets provide Year 4 students with ample opportunities to practice and improve their understanding of this crucial topic. Teachers can use these worksheets as part of their lesson plans, homework assignments, or even as supplementary material for students who may need extra support. With the help of these Perimeter of a Rectangle worksheets for Year 4, teachers can ensure that their students develop a strong foundation in Math and Geometry, setting them up for success in future grades.

In addition to Perimeter of a Rectangle worksheets for Year 4, Quizizz offers a wide range of resources and tools that can help teachers enhance their students’ learning experience. Quizizz is an online platform that allows teachers to create and share interactive quizzes, worksheets, and other educational materials with their students. By incorporating Quizizz into their lesson plans, teachers can provide a more engaging and interactive learning environment for their Year 4 students. The platform also offers a variety of pre-made quizzes and worksheets, covering topics such as Math, Geometry, and Perimeter, which can save teachers valuable time and effort. Furthermore, Quizizz allows teachers to track their students’ progress and performance, enabling them to identify areas where students may need additional support or practice. By utilizing Quizizz and its vast array of resources, teachers can ensure that their Year 4 students receive a well-rounded education in Math and Geometry, including the crucial concept of perimeter.

Worksheet on Area and Perimeter of Rectangles

Refer to Worksheet on Area and Perimeter of Rectangles while preparing for the exam. You can perform well by practicing various questions from Rectangle Area and Perimeter Worksheets. Multiple models of questions along with the detailed solutions are given here. This Area and Perimeter of Rectangles Worksheet are designed as per the latest syllabus. So, students can learn the rectangles topic and score well in the examinations. Check out all the questions and rectangle area, rectangle perimeter formulas in the following sections of this page.

1. Find the perimeter and area of the following rectangles whose dimensions are:

(i) length = 11 cm, breadth = 5 cm

(ii) length = 6.7 cm, breadth = 5.1 cm

(iii) length = 14 m, breadth = 6 m

(iv) length = 8 feet, breadth = 3 feet

Solution:

(i)

Given that,

length = 11 cm, breadth = 5 cm

Rectangle Area = length x breadth

= 11 x 5 = 55 cm²

Rectangle Perimeter = 2(length + breadth)

= 2(11 + 5) = 16 x 2 cm

= 32 cm

ˆ´ The Rectangle area is 55 cm², perimeter is 32 cm.

(ii)

Given that,

length = 6.7 cm, breadth = 5.1 cm

Rectangle Area = length x breadth

= 6.7 x 5.1 = 34.17 cm²

Rectangle Perimeter = 2(length + breadth)

= 2(6. 7 + 5.1) = 2 x 11.8 cm

= 23.6

ˆ´ The Rectangle area is 34.17 cm², perimeter is 23.6 cm.

(iii)

Given that,

length = 14 m, breadth = 6 m

Rectangle Area = length x breadth

= 14 x 6 = 84 m²

Rectangle Perimeter = 2(length + breadth)

= 2(14 + 6) = 20 x 2 = 40 m

ˆ´ The Rectangle area is 84 m², perimeter is 40 m.

(iv)

Given that,

length = 8 feet, breadth = 3 feet

Rectangle Area = length x breadth

= 8 x 3 = 24 sq feet

Rectangle Perimeter = 2(length + breadth)

= 2(8 + 3) = 11 x 2 = 22 feet

ˆ´ The Rectangle area is 24 sq feet, perimeter is 22 feet.

2. The area of a rectangle is 92 m², its length is 8 m. Find the rectangle breadth and perimeter?

Solution:

Given that,

Rectangle area = 92 m²

Rectangle length = 8 m

The rectangle area formula is

Area = length x breadth

So, breadth = area / length

Breadth = 92 / 8

= 11. 5 m

Rectangle Perimeter = 2(Length + breadth)

= 2(8 + 11.5) = 2(19.5) = 39 m

ˆ´ The Rectangle breadth is 11.5 m, perimeter is 39 m.

3. If the rectangle perimeter is 28 cm, its width is 18 cm. Find the rectangle length and area?

Solution:

Given that,

Rectangle Perimeter p = 28 cm

Width w = 18 cm

Rectangle perimeter p = 2(l + w)

28 = 2l + 36

2l = 28 – 36

2l = 8

l = 8/2

l = 4 cm

Rectangle area A = (l x w)

= 18 x 4 = 72 cm²

ˆ´ The Rectangle length is 4 cm, area is 72 cm².

4. Find the cost of tiling a rectangular plot of land 250 m long and 500 m wide at the rate of $8 per hundred square m?

Solution:

Given that,

The rectangular plot length = 250 m

Rectangular plot width = 500 m

Area of rectangular polt = length x width

= 250 x 500 = 125000 sq. m

Cost of tiling = $8 per 100 sq. m = $8/100 per 1 sq. m

Cost of tiling of rectangular polt of 125000 sq. m = (8/100) x 125000 = 10,000

ˆ´ The cost of tiling of the rectangular plot is Rs. 10,000/-.

5. A room is 4 feet long and 6 feet wide. How many square feet of carpet is needed to cover the floor of the room?

Solution:

Given that,

Rectangle length l = 4 feet

Rectangle width w = 6 feet

Area of the rectangle A = l x w

A = 4 x 6

A = 24 sq feet

So, 24 sq feet of carpet is needed to cover the room floor.

6. A table-top measures 5 m by 3 m 50 cm. What is the area and perimeter of the table?

Solution:

Given that,

Table length l = 5 m

width w = 3 m 50 cm

= 3 + 50 x (1/100)

= 3 + 1/2

= 7/2 = 3.5 m

Table Perimeter p = 2(l + w)

= 2(5 + 3.5) = 2(8.5) m

= 17 m

Table area A = l x w

A = 5 x 3.5

= 17.5 m²

ˆ´ The table area is 17.5 m², the perimeter is 8.5 m.

7. A floor is 25 m long and 14 m wide. A square carpet of sides 8 m is laid on the floor. Find the area of the floor that is not carpeted and floor perimeter?

Solution:

Given that,

Rectangular floor-length l = 25 m

Rectangular floor breadth b = 14 m

Square carpet side s = 8 m

Rectangular floor area A = l x b

A = 25 x 14

A = 350 m²

Area of the square carpet a = s x s

a = 8 x 8

a = 64 m²

Area of the floor that is not carpeted = Rectangular floor area – Area of the square carpet

= A – a = 350 – 64

= 286 m²

Rectangular flooe perimeter P = 2(l + b)

P = 2(25 + 14)

P = 2(39) = 78 m

ˆ´ Area of the floor that is not carpeted is 286 m², rectangular floor perimeter is 39 m.

8. How many tiles whose length and breadth are 15 cm and 6 cm respectively are needed to cover a rectangular region whose length and breadth are 510 cm and 135 cm?

Solution:

Given that,

Length of the tile l = 15 cm

Breadth of the tile b = 6 cm

Rectangular region length = 510

Rectangular region breadth = 135

Area of the tiles = l x b

= 15 x 6 = 90 cm²

Area of the plot = 510 x 135

= 68,850 cm²

Number of tiles required = Area of plot / Area of tiles

= 68850 / 90

= 765

Therefore, the required number of tiles are 765.

9. How many rectangles can be drawn with 22 cm as a perimeter? Also, find the dimensions of the rectangle whose area will be maximum?

Solution:

Given that,

The perimeter of the rectangle = 22 cm

2(l + w) = 22

(l + w) = 22/2

= 11

Possible dimensions of the rectangle are (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (10, 1), (9, 2), (8, 3), (7, 4).

ˆ´ The dimensions of the rectangle whose area is maximum is (6, 5) or (5, 6) and 11 rectangles can be drawn.

10. The perimeter of a rectangular pool is 140 m, and its length is 60 m. Find the pool width and area?

Solution:

The rectangular pool perimeter p = 140 m

Rectangular pool length l = 60 m

Rectangular pool width w = ?

Rectangular pool perimeter p = 2(l + w)

140 = 2(60 + w)

140 = 120 + 2w

2w = 140 – 120

2w = 20

w = 20/2

w = 10

Rectangular pool area A = l x w

A = 60 x 10

A = 600

ˆ´ The rectangular pool width is 10 m, area is 600 m².

11. The length of a rectangular wooden board is four times its width. If the width of the board is 155 cm, find the cost of framing it at the rate of $5 for 20 cm?

Solution:

Given that,

Width of a rectangular wooden board w = 155 cm

The cost of framing = $5 for 20 cm

The length of a rectangular wooden board l = 4w

l = 4 x 155

l = 620

Wooden board perimeter P = 2(l + w)

P = 2(620 + 155)

= 2(775) = 1550

The cost of framing = $5/20 for 1 cm

The cost of wooden board framing = 1550 x (5/20)

= 7750/20

= 387.5

ˆ´ The cost of framing is $387.5.

Perimeter and area of a rectangle. Perimeter and area of a rectangle What is the formula to find the perimeter of a rectangle

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 do without the perimeter formula and the skills to calculate it.

Basic concepts

A rectangle is a quadrilateral in which all angles are right and opposite sides are equal and parallel in pairs. In our life, many figures are in the shape of a rectangle, for example, the surface of a table, a notebook, and so on.

Consider an example:
it is necessary to put a fence along the boundaries of the land plot. In order to find out the length of each side, you need to measure them.

Fig. 1. Land plot in the shape of a rectangle.

The land plot has sides with a length of 2 m., 4 m., 2 m., 4 m. therefore, to find out the total length of the fence, you must add the lengths of all sides:

2+2+4+4= 2 2+4 2 =(2+4) 2 =12 m.

It is this value that is generally called the perimeter. Thus, to find the perimeter, you need to add all the sides of the figure. The letter P is used to designate the perimeter.

To calculate the perimeter of a rectangular figure, you do not need to divide it into rectangles, you need to measure only 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 are 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 system of measurement.

Figure Perimeter Formula

If we take into account the fact that the opposite sides of the rectangle are equal, then we can derive the formula for the perimeter of the rectangle:

$P = (a+b) * 2$, where a, b are the sides of the figure.

Fig. 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 \u200b\u200bthe figure, you can use to express the other side through the area. Then the formula will look like this:

$P = {{2S + 2a2}\over{a}}$, where S is the area of the rectangle.

Fig. 3. Rectangle with sides a, b.

Job

: Calculate the perimeter of a rectangle if its sides are 4 cm and 6 cm.

Solution:

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 the sides of a figure, the semi-perimeter is the sum of only one length and width. Multiply the semi-perimeter by 2 to get the perimeter.

Area and perimeter are the 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.

What have we learned?

We have learned how to find the perimeter of a rectangle. And also got acquainted with the formula for its calculation. This topic can be encountered not only when solving mathematical problems, but also in real life.

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In this lesson we will get acquainted with a new concept — the perimeter of a rectangle. We formulate the definition of this concept, derive a formula for its calculation. We also repeat the associative law of addition and the distributive law of multiplication.

In this lesson we will learn about the perimeter of a rectangle and its calculation.

Consider the following geometric figure (Fig. 1):

Fig. 1. Rectangle

This shape is a rectangle. Let’s recall what distinctive features of a rectangle we know.

A rectangle is a quadrilateral whose four right angles and sides are equal in pairs.

What can be rectangular in our lives? For example, a book, a tabletop, or a piece of land.

Consider the following problem:

Task 1 (Fig. 2)

Builders needed to put up a fence around the land plot. The width of this section is 5 meters, the length is 10 meters. What length of fence will the builders get?

Fig. 2. Illustration for problem 1

The fence is placed along the boundaries of the site, therefore, in order to find out the length of the fence, you need to know the length of each side. This rectangle has sides equal: 5 meters, 10 meters, 5 meters, 10 meters. Let’s make an expression for calculating the length of the fence: 5 + 10 + 5 + 10. Let’s use the commutative law of addition: 5+10+5+10=5+5+10+10. In this expression, there are sums of identical terms (5 + 5 and 10 + 10). Let’s replace the sums of identical terms with products: 5+5+10+10=5 2+10 2. Now let’s use the distributive law of multiplication with respect to addition: 5·2+10·2=(5+10)·2.

Find the value of the expression (5+10) 2. First, we perform the action in brackets: 5+10=15. And then we repeat the number 15 twice: 15 2=30.

Answer: 30 meters.

Rectangle perimeter
is the sum of the lengths of all its sides. Formula for calculating the perimeter of a rectangle
: , where a is the length of the rectangle and b is the width of the rectangle. The sum of the length and width is called semi-perimeter
. To get the perimeter from the semi-perimeter, you need to increase it by 2 times, that is, multiply by 2.

Let’s use the rectangle perimeter formula and find the perimeter of a rectangle with sides 7 cm and 3 cm: (7+3) 2=20 (cm).

The perimeter of any figure is measured in linear units.

In this lesson, we got acquainted with the perimeter of a rectangle and the formula for calculating it.

The product of a number and the sum of numbers is equal to the sum of the products of the given number and each of the terms.

If the perimeter is the sum of the lengths of all sides of a figure, then the semi-perimeter is the sum of one length and one width. We find the semi-perimeter when we work on the formula for finding the perimeter of a rectangle (when we perform the first operation in brackets — (a + b)).

References

Aleksandrova E. I. Mathematics. Grade 2 — M.: Drofa, 2004.
Bashmakov M.I., Nefyodova M.G. Mathematics. Grade 2 — M.: Astrel, 2006.
Dorofeev G.V., Mirakova T.I. Mathematics. Grade 2 — M.: Education, 2012.

Festival.1september.ru ().
Nsportal.ru ().
Math-prosto.ru ().

Homework

Find the perimeter of a rectangle whose length is 13 meters and width is 7 meters.
Find the half-perimeter of a rectangle if its length is 8 cm and its width is 4 cm.
Find the perimeter of a rectangle if its half-perimeter is 21 dm.

The rectangle has many distinctive features, on the basis of which the rules for calculating its various numerical characteristics have been developed. So, rectangle:

Flat geometric figure;
Quadrilateral;
A figure in which opposite sides are equal and parallel, all angles are right.

The perimeter is the total length of all sides of the figure.

Calculating the perimeter of a rectangle is a fairly simple task.

All you need to know is the width and length of the rectangle. Since the rectangle has two equal lengths and two equal widths, only one side is measured.

The perimeter of a rectangle is twice the sum of its 2 sides length and width.

P = (a + b) 2, where a is the length of the rectangle, b is the width of the rectangle.

The perimeter of a rectangle can also be found using the sum of all sides.

P= a+a+b+b, where a is the length of the rectangle, b is the width of the rectangle.

The perimeter of a square is the length of the side of the square multiplied by 4.

P = a 4, where a is the length of the side of the square.

Supplement: Finding find area and perimeter of rectangles

The curriculum for grade 3 provides for the study of polygons and their features. In order to understand how to find the perimeter of a rectangle and the area, let’s figure out what is meant by these concepts.

Basic concepts

Finding the perimeter and area requires knowledge of some terms. These include:

Right angle. It is formed from 2 rays having a common origin in the form of a point. When getting acquainted with the figures (grade 3), the right angle is determined using a square.
Rectangle. It is a quadrilateral with all right angles. Its sides are called length and width. As you know, the opposite sides of this figure are equal.
Square. It is a quadrilateral with all sides equal.

When learning about polygons, their vertices may be called ABCD. In mathematics, it is customary to name points in drawings with letters of the Latin alphabet. The name of the polygon lists all vertices without gaps, for example, triangle ABC.

Perimeter calculation

The perimeter of a polygon is the sum of the lengths of all its sides. This value is denoted by the Latin letter P. The level of knowledge for the proposed examples is grade 3.

Problem 1: “Draw a rectangle 3 cm wide and 4 cm long with vertices ABCD. Find the perimeter of rectangle ABCD.

The formula will look like this: P=AB+BC+CD+AD or P=AB×2+BC×2.

Answer: P=3+4+3+4=14 (cm) or P=3×2 + 4×2=14 (cm).

Problem 2: «How to find the perimeter of a right triangle ABC if the sides are 5, 4 and 3 cm?».

Answer: P=5+4+3=12 (cm).

Problem 3: «Find the perimeter of a rectangle with one side 7 cm long and the other 2 cm longer.»

Answer: P=7+9+7+9=32 (cm).

Task No. 4: “Swimming competitions were held in a pool with a perimeter of 120 m. How many meters did the participant swim if the pool was 10 m wide?”.

In this problem, the question is how to find the length of the pool. Find the lengths of the sides of the rectangle to solve. The width is known. The sum of the lengths of the two unknown sides should be 100 m. 120-10×2=100. To find out the distance covered by the swimmer, you need to divide the result by 2. 100:2=50.

Answer: 50 (m).

Area calculation

A more complex value is the area of the figure. Measures are used to measure it. The standard among measurements are squares.

The area of a square with a side of 1 cm is 1 cm². The square decimeter is denoted as dm², and the square meter is denoted as m².

Applications for units of measure can be as follows:

cm² measures small objects such as photographs, textbook covers, sheets of paper.
In dm² you can measure a geographical map, window glass, a picture.
To measure the floor, apartment, land use m².

If you draw a rectangle 3 cm long and 1 cm wide and divide it into squares with a side of 1 cm, then 3 squares will fit in it, which means its area will be 3 cm². If the rectangle is divided into squares, we can also find the perimeter of the rectangle without difficulty. In this case, it is 8 cm.

Another way to count the number of squares that fit into a shape is to use a palette. Let’s draw on a tracing paper a square with an area of 1 dm², which is 100 cm². Let’s place a tracing paper on the figure and count the number of square centimeters in one row. After that, find out the number of rows, and then multiply the values. So the area of a rectangle is the product of its length and width.

Area comparison methods:

Eye. Sometimes just looking at the objects is enough, because in some cases it can be seen with the naked eye that one figure takes up more space, like, for example, a textbook lying on the table next to the pencil case.
Overlay. If the figures coincide when superimposed, their areas are equal. If one of them completely fits inside the second, then its area is smaller. The space occupied by a notebook sheet and a page from a textbook can be compared by superimposing them on top of each other.
By the number of measures. When superimposed, the figures may not coincide, but have the same area. In this case, you can compare by counting the number of squares into which the figure is divided.
Numbers. Compare numerical values measured with the same measure, for example, in m².

Example 1: “A seamstress sewed a baby blanket from square patches of different colors. One shred 1 dm long, in a row of 5 pieces. How many decimeters of tape will a seamstress need to finish the edges of a blanket if the area is known to be 50 dm²?

To solve the problem, you need to answer the question of how to find the length of a rectangle. Next, find the perimeter of a rectangle made up of squares. It is clear from the problem that the width of the blanket is 5 dm, we calculate the length by dividing 50 by 5, and we get 10 dm. Now find the perimeter of a rectangle with sides 5 and 10. P=5+5+10+10=30.

Answer: 30 (m).

Example #2: “During the excavations, a site was discovered where ancient treasures may be located. How much territory will scientists have to explore if the perimeter is 18 m and the width of the rectangle is 3 m?

Determine the length of the section by doing 2 steps. 18-3×2=12. 12:2=6. The desired area will also be equal to 18 m² (6 × 3 = 18).

Answer: 18 (m²).

Thus, knowing the formulas, it will not be difficult to calculate the area and perimeter, and the above examples will help you practice solving mathematical problems.

The ability to find the perimeter of a rectangle is very important for solving many geometric problems. Below is a detailed instruction on finding the perimeter of different rectangles.

How to find the perimeter of an ordinary rectangle

A regular rectangle is a quadrilateral with equal parallel sides and all angles = 90º. There are 2 ways to find its perimeter:

Add up all sides.

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

Decision (sequence of actions and reasoning):

Since we know the width and length of the rectangle, finding its perimeter is not difficult. The width is parallel to the width, and the length is the length. Thus, in a regular rectangle, there are 2 widths and 2 lengths.
Add up all sides (3 + 3 + 6 + 6) = 18 cm.

Answer: P = 18 cm.

The second way is as follows:

It is necessary to add the width and length, and multiply by 2. The formula for this method is as follows: 2 × (a + b), where a is the width, b is the length.

Within the framework of this task, we obtain the following solution:

2×(3 + 6) = 2×9 = 18.

Answer: P = 18.

How to find the perimeter of a rectangle — a square

Square is a regular quadrilateral. Correct because all its sides and angles are equal. There are also two ways to find its perimeter:

Add up all its sides.
Multiply its side by 4.

Example: Find the perimeter of a square if its side = 5 cm.

Since we know the side of the square, we can find its perimeter.

Add all sides: 5 + 5 + 5 + 5 = 20.

Answer: P = 20 cm.

Multiply the side of the square by 4 (because everyone is equal): 4×5 = 20.

Answer: P = 20 cm.

How to Find the Perimeter of a Rectangle — Online Resources

While the above steps are easy to understand and master, there are several online calculators that can help you calculate the perimeters (area, volume) of various shapes. Just type in the required values and the mini-program will calculate the perimeter of the shape you need. Below is a short list.

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

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

Rectangle features

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

How to calculate the perimeter of a rectangle

There are 2 ways to find it:

1 way.
Add up all sides. P = a + a + b + b
2 way.
Add width and length, and multiply by 2. P = (a + b) 2.
OR R = 2 a + 2 b.
Sides of a rectangle that lie opposite each other (opposite) are called length and width.

«a»
— the length of the rectangle, the longer pair of its sides.

«b»
— the width of the rectangle, the shorter pair of its sides.

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

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

Memorize the formulas for calculating the perimeter of a rectangle!

Semi Perimeter
is the sum of one length and one width .

Rectangle half perimeter —
when doing the first action in brackets — (a+b)
.
To obtain a perimeter from a semi-perimeter, you need to increase it by 2 times, i.e. multiply by 2.

How to find the area of a rectangle

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

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

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

Remember!

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

How to solve problems on finding the perimeter, area and volume of figures in grades 4-5

PERIMETER

Perimeter is the sum of the lengths of all sides of a flat geometric figure. Most often, the perimeter is measured in centimeters, meters and kilometers.

The most common designation for the perimeter is P .

Perimeter of a rectangle — twice the sum of the length and height — 2∙(a+b)

The perimeter of a square is the product of any of its sides by 4, since the sides are equal.

AREA

Area is a characteristic of a closed geometric figure that shows its size. Most often, the area is measured in square centimeters, square meters and square kilometers.

Unlike the perimeter, there is no universal area formula. For each type of figure, the area is calculated using its own special formula. We will consider only rectangles, squares, and composite shapes made up of rectangles and squares.

The most common designation for an area is S .

The area of a rectangle is the product of length and height.

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Our VIDEO COURSE will help you

Divide this rectangle into squares

We got 15 squares inside this rectangle — these are the same 15 square centimeters that make up the area of the rectangle.

The area of a square is the product of the length of a side and itself.

COMPOSITE FIGURES

Divide this figure into a rectangle and a square

The height of the rectangle will be 5 — 3 = 2

AREA AND PERIMETER RATIO

Figures with the same area can have different perimeters

Why did the perimeter change, although the area, i. e. the number of squares inside the figure remained the same?

Because the number of faces of the squares that participate in the formation of the sides of the figure has changed, i.e. permeter. In the first figure — a large square, two outer faces of each small square participated in the formation of the sides — the total number of such faces is 8, and the perimeter is 8.

In the second figure, we have three faces at the two outer squares and two faces of the inner squares in the formation of the sides. The total number of such faces is 10, and the perimeter is 10.

VOLUME

Volume is a quantitative characteristic of the space occupied by a body or substance. Most often, volume is measured in cubic centimeters, cubic decimeters, cubic meters and liters.

1 l = 1 dm ³

There is no universal volume formula. For each type of figure, the volume is calculated using its own special formula. We will consider only rectangular parallelepipeds.

Most often, the volume is indicated by the letter V .

Rectangular box is a closed figure with 6 rectangular faces (front, back, bottom, top and two side), and each face is at right angles to its neighbors.

The volume of a cuboid is the product of its length, width and height

Knowing the volume and two sides, we can find the third side:

c = (V:a):b = V:S

VIDEO COURSE 2plus2.online on solving olympiad problems in mathematics for grade 4 and problems from entrance exams to the 5th grade of the physics and mathematics school.

PROBLEM

Problem 1. Find the perimeter and area of a rectangle whose width is 10 cm and is less than the length by 6 cm.

x = 10 cm — width

1. Find the length

y = 10 + 6 = 16 cm

2. Find the perimeter

P = 2∙(10+16) = 52 cm

3. Find the area

S = 10∙16 = 160 cm ²

Answer: P = 52 cm, S = 160 cm ²

Problem 2. What is the width of a rectangle with a length of 50 cm and an area equal to the area of a square with a perimeter of 80 cm?

1. Calculate the side of the square

4∙n = 80 — perimeter

n = 20 cm

2. Calculate the area of the square

20∙20 = 400 cm ²

3. Calculate the width of the rectangle

50∙x = 400 cm ²
x = 8 cm

Answer: 8 cm

Problem 3. What is the width of a rectangle with a length of 15 m and an area of 7500 dm2?

1 dm = 10 cm, 1 m = 100 cm, 1 m = 10 dm

1. Convert the length of the rectangle to dm

x = 15∙10 = 150 dm

2. Find the width of the rectangle

150∙y = 7500

y = 7500:150 = 50 dm

Answer: 50 dm

Problem 4. The length of the rectangle is 60 cm, and it is 3 times the width of the side.

1. Find the area of this rectangle.

2. Find the area of a square that has the same perimeter as the rectangle.

3. Find the perimeter of a square whose area is 12 times smaller than the area of the rectangle.

1. Find the width of the rectangle

x = 60:3 = 20 cm

2. Find the area of the rectangle

S = 60∙20 = 1200 cm

2. Find the perimeter of the rectangle

P = 2∙(60+20) = 160 cm

3. Find the side of the square

y = 160:4 = 40 cm

4. Find the area of the square

Sq = 40∙40 = 1600 cm ²

5. Find the area of the square, which is 12 times less than the area of the rectangle:

SQ ₂ = 1200:12 = 100 cm ²

6. Find the side of such a square

Square area = 100 cm ²
From the multiplication table we know that 10∙10 = 100, so the side of the square = 10 cm

7. Find the perimeter of such a square

P = 10∙4 = 40 cm

VIDEO COURSE 2plus2. online on solving olympiad problems in mathematics for grade 4 and problems from entrance exams to the 5th grade of the physical school.

Problem 5. In a rectangle ABCD, side AB is 3 cm, side BC is 1 cm longer, and diagonal BD is 2 cm longer than AB. Find the perimeter and area of rectangle ABCD and triangle ABCD.

1. Find the side BC

BC = 3+1 = 4

2. Find the diagonal of the VD

ID = 3+2 = 5

3. Find the perimeter of ABCD

P = 2∙(3+4) = 14 cm

4. Find the area of ABCD

Savsd \u003d 3 4 \u003d 12 cm ²

5. Find the perimeter of the triangle AED

Pavd = 3 + 5 + 4 = 13 cm

6. Find the area of triangle ABD

Triangle ABD occupies half the area of rectangle ABCD

Savd = Savd:2

Savd = 12:2 = 6 cm ²

Task 6 . In an aquarium in the form of a rectangular parallelepiped, the base of which has sides of 80 and 40 cm, 160 liters of water were poured to the brim.

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