What you need to do is find the area of the rectangle. How to calculate the area of a rectangle: practical tips
Square geometric figure - a numerical characteristic of a geometric figure showing the size of this figure (part of the surface bounded by a closed contour of this figure). The size of the area is expressed by the number of square units contained in it.
Triangle area formulas
- Triangle area formula for side and height
Area of a triangle equal to half the product of the length of a side of a triangle and the length of the altitude drawn to this side - The formula for the area of a triangle given three sides and the radius of the circumscribed circle
- The formula for the area of a triangle given three sides and the radius of an inscribed circle
Area of a triangle is equal to the product of the half-perimeter of the triangle and the radius of the inscribed circle. where S is the area of the triangle,
- the lengths of the sides of the triangle,
- the height of the triangle,
- the angle between the sides and,
- radius of the inscribed circle,
R - radius of the circumscribed circle,
Square area formulas
- The formula for the area of a square given the length of a side
square area is equal to the square of its side length. - The formula for the area of a square given the length of the diagonal
square area equal to half the square of the length of its diagonal.S= 1 2 2 where S is the area of the square,
is the length of the side of the square,
is the length of the diagonal of the square.
Rectangle area formula
- Rectangle area is equal to the product of the lengths of its two adjacent sides
where S is the area of the rectangle,
are the lengths of the sides of the rectangle.
Formulas for the area of a parallelogram
- Parallelogram area formula for side length and height
Parallelogram area - The formula for the area of a parallelogram given two sides and the angle between them
Parallelogram area is equal to the product of the lengths of its sides multiplied by the sine of the angle between them.a b sinα
where S is the area of the parallelogram,
are the lengths of the sides of the parallelogram,
is the height of the parallelogram,
is the angle between the sides of the parallelogram.
Formulas for the area of a rhombus
- Rhombus area formula given side length and height
Rhombus area is equal to the product of the length of its side and the length of the height lowered to this side. - The formula for the area of a rhombus given the length of the side and the angle
Rhombus area is equal to the product of the square of the length of its side and the sine of the angle between the sides of the rhombus. - The formula for the area of a rhombus from the lengths of its diagonals
Rhombus area is equal to half the product of the lengths of its diagonals. where S is the area of the rhombus,
- length of the side of the rhombus,
- the length of the height of the rhombus,
- the angle between the sides of the rhombus,
1, 2 - the lengths of the diagonals.
Trapezium area formulas
- Heron's formula for a trapezoid
Where S is the area of the trapezoid,
- the length of the bases of the trapezoid,
- the length of the sides of the trapezoid,
A rectangle is a special case of a quadrilateral. This means that the rectangle has four sides. Its opposite sides are equal: for example, if one of its sides is 10 cm, then the opposite side will also be 10 cm. A special case of a rectangle is a square. A square is a rectangle with all sides equal. To calculate the area of a square, you can use the same algorithm as for calculating the area of a rectangle.
How to find the area of a rectangle on two sides
To find the area of a rectangle, multiply its length by its width: Area = Length × Width. In the case below: Area = AB × BC.
How to find the area of a rectangle given the side and length of the diagonal
In some problems, you need to find the area of a rectangle using the length of the diagonal and one of the sides. The diagonal of a rectangle divides it into two equal right triangles. Therefore, you can determine the second side of the rectangle using the Pythagorean theorem. After that, the problem is reduced to the previous point.
How to find the area of a rectangle by perimeter and side
The perimeter of a rectangle is the sum of all its sides. If you know the perimeter of the rectangle and one side (for example, the width), you can calculate the area of the rectangle using the following formula:
Area \u003d (Perimeter × Width - Width ^ 2) / 2.
Area of a rectangle in terms of the sine of an acute angle between the diagonals and the length of the diagonal
The diagonals in a rectangle are equal, so to calculate the area based on the length of the diagonal and the sine of the acute angle between them, use the following formula: Area = Diagonal^2 × sin(acute angle between the diagonals)/2.
The area of a rectangle is not going to sound cocky, but it's an important concept. IN Everyday life we are constantly confronted with it. Find out the size of fields, vegetable gardens, calculate the amount of paint needed for whitewashing the ceiling, how much wallpaper is needed for pasting co
mints and more.
Geometric figure
First, let's talk about the rectangle. This is a figure on a plane that has four right angles, and its opposite sides are equal. Its sides are used to be called length and width. They are measured in millimeters, centimeters, decimeters, meters, etc. Now let's answer the question: "How to find the area of a rectangle?" To do this, you need to multiply the length by the width.
Area=length*width
But one more caveat: length and width must be expressed in the same units of measurement, that is, meter and meter, not meter and centimeter. The area is written with the Latin letter S. For convenience, we denote the length with the Latin letter b, and the width with the Latin letter a, as shown in the figure. From this we conclude that the unit of area is mm 2, cm 2, m 2, etc.
Let's look at a specific example of how to find the area of a rectangle. Length b=10 units Width a=6 units Solution: S=a*b, S=10 units*6 units, S=60 units 2 . Task. How to find the area of a rectangle if the length is 2 times the width and is 18 m? Solution: if b=18 m, then a=b/2, a=9 m. How to find the area of a rectangle if both sides are known? That's right, plug it into the formula. S=a*b, S=18*9, S=162 m2. Answer: 162 m 2. Task. How many rolls of wallpaper do you need to buy for a room if its dimensions are: length 5.5 m, width 3.5, and height 3 m? Wallpaper roll dimensions: length 10 m, width 50 cm. Solution: draw a drawing of the room.
The areas of opposite sides are equal. Calculate the area of the wall with dimensions of 5.5 m and 3 m. S wall 1 = 5.5 * 3,
S wall 1 \u003d 16.5 m 2. Therefore, the opposite wall has an area of 16.5 m2. Find the area of the next two walls. Their sides, respectively, are 3.5 m and 3 m. S walls 2 \u003d 3.5 * 3, S walls 2 \u003d 10.5 m 2. Hence, the opposite side is equal to 10.5 m 2. Let's add up all the results. 16.5 + 16.5 + 10.5 + 10.5 \u003d 54 m 2. How to calculate the area of a rectangle if the sides are expressed in different units. Previously, we calculated the area in m 2, then in this case we will use meters. Then the width of the wallpaper roll will be 0.5 m. S roll \u003d 10 * 0.5, S roll \u003d 5 m 2. Now we will find out how many rolls are needed for pasting a room. 54:5=10.8 (rolls). Since they are measured in whole numbers, you need to buy 11 rolls of wallpaper. Answer: 11 rolls of wallpaper. Task. How to calculate the area of a rectangle if you know that the width is 3 cm shorter than the length, and the sum of the sides of the rectangle is 14 cm? Solution: let the length be x cm, then the width (x-3) cm. x+(x-3)+x+(x-3)=14, 4x-6=14, 4x=20, x=5 cm - length rectangle, 5-3 \u003d 2 cm - the width of the rectangle, S \u003d 5 * 2, S \u003d 10 cm 2 Answer: 10 cm 2.
Summary
Having considered the examples, I hope it became clear how to find the area of a rectangle. Let me remind you that the units of measurement for length and width must match, otherwise you will get an incorrect result, in order to avoid mistakes, read the task carefully. Sometimes a side can be expressed through the other side, don't be afraid. Refer to our solved problems, it is quite possible they can help. But at least once in a lifetime we are faced with finding the area of a rectangle.
is a parallelogram in which all angles are 90° and opposite sides are pairwise parallel and equal.
The rectangle has several irrefutable properties that are used in solving many problems, in the formulas for the area of \u200b\u200bthe rectangle and its perimeter. Here they are:
The length of the unknown side or diagonal of the rectangle is calculated by or by the Pythagorean theorem. The area of a rectangle can be found in two ways - by the product of its sides or by the formula for the area of \u200b\u200ba rectangle through the diagonal. The first and simplest formula looks like this:
An example of calculating the area of a rectangle using this formula is very simple. Knowing the two sides, for example a = 3 cm, b = 5 cm, we can easily calculate the area of the rectangle:
We get that in such a rectangle the area will be equal to 15 square meters. cm.
Area of a rectangle in terms of diagonals
Sometimes you need to apply the formula for the area of a rectangle in terms of diagonals. For it, you will need not only to know the length of the diagonals, but also the angle between them:
Consider an example of calculating the area of a rectangle using diagonals. Let a rectangle with diagonal d = 6 cm and angle = 30° be given. We substitute the data in the already known formula:
So, the example of calculating the area of a rectangle through the diagonal showed us that finding the area in this way, given the angle, is quite simple.
Consider another interesting puzzle that will help us stretch our brains a little.
Task: Given a square. Its area is 36 sq. cm. Find the perimeter of a rectangle whose length of one of its sides is 9 cm, and the area is the same as that of the square given above.
So we have a few conditions. For clarity, we write them down to see all known and unknown parameters: 
The sides of the figure are pairwise parallel and equal. Therefore, the perimeter of the figure is equal to twice the sum of the lengths of the sides:
From the formula for the area of a rectangle, which is equal to the product of the two sides of the figure, we find the length of the side b
From here:
We substitute the known data and find the length of the side b:
Calculate the perimeter of the figure: 
So, knowing a few easy formulas, you can calculate the perimeter of a rectangle, knowing its area.
L * H = S to find the area of a rectangle, you need to multiply the width by the length. In other words, it can be expressed like this: the area of a rectangle is equal to the product of the sides.
1. Let's give an example of calculation how to find the area of a rectangle, the sides are equal to known values, for example, width 4 cm, length 8 cm.
How to find the area of a rectangle with sides 4 and 8 cm: The solution is simple! 4 x 8 = 32 cm2. To solve such a simple problem, you need to calculate the product of the sides of the rectangle or simply multiply the width by the length, this will be the area!
2. A special case of a rectangle is a square, this is the case when the sides of the rectangle are equal, in this case, you can find the area of the square using the above formula.
What is the area of the rectangle?
The ability to calculate the area of a rectangle is a basic skill for solving a huge number of everyday or technical problems. This knowledge is applied in almost all areas of life! For example, in cases where areas of any surfaces are needed in construction or real estate. When calculating the areas of land, plots, walls of houses, residential premises ... it is not possible to name a single area of human activity where this knowledge cannot be useful!
If calculating the area of a rectangle causes you difficulties - just use our calculator! O will immediately bring all the necessary calculations and write the text of the decision with explanations in detail.