In geometry lessons, many new topics are held, one of them is how to find the area of \u200b\u200ba rectangle. After the assimilation of the formulas, tasks are given to consolidate the material. In this article we will learn how to find the area of \u200b\u200bthe rectangle and consider some examples on this topic.
Content
At school, not everyone is able to learn the material that the teacher tells in the lesson. Therefore, at home you should still practice and study what was not clear in the lesson. Otherwise, in the future, missed topics will not be learned in the student’s head and there will be large knowledge gaps. Formulas should be known by heart, so you can easily solve geometry problems. How to find the area of \u200b\u200ba rectangle - we will find out further.
How to find the area of \u200b\u200ba rectangle - what is a rectangle?
Before starting to study the main material, you should figure out what a rectangle is for a figure. Thanks to such knowledge, it will be clear how to find its area. So, a figure with four straight angles and equal opposite sides is called rectangle. As can be seen from the rule that in a rectangle, all angles are 90º and the opposite sides are equal to each other. This statement will be applied for evidence of certain theorems. Moreover, the long sides of the rectangle are the length of the figure, and those sides that are smaller - are a height.
IMPORTANT: Not all figures with four corners can be rectangles.
And the rectangles have certain properties that characterize them, in particular:
- The parties that are opposite each other parallel to each other.
- The lines drawn from the opposite angles of the rectangle - the diagonals have the same length, and the intersection point divides them into equal segments.
- This point in the rectangle is also called - the center, relatively symmetrical. All other points that are at the same distance from each other.
- Do not also confuse a rectangle with a parallelogram and a square. The first corners are not 90º, and the second absolutely all sides are equal. We can also say that a rectangle is a square and parallelograms, it is suitable for some characteristics of these figures.
Rectangle area - basic formula
If the properties of a rectangle have already been passed, then you can begin to study the formulas. The area of \u200b\u200bthe rectangle is calculated by the formula:
S \u003d A • B and measured in square units.
Where s is the area, and the sides, or rather, the length and height of the figure is: a and b.
For example, the amnk rectangle with a length mn \u003d 8 cm and the height AM \u003d 5 cm will have an area:
S \u003d mN • am \u003d 8 • 5 \u003d 40 cm²
Proof of the basic formula of the area of \u200b\u200bthe rectangle
The area of \u200b\u200bthe rectangle is a certain value that shows how much space is required for a given figure on the plane. If the geometric figure is divided into small zones with one centimeter, as in the image below, then you can easily calculate the value of the area in centimeters of the square.
In the rectangle, which is higher in the picture of a total of 15 squares. That is, its area is 15 cm². And the picture shows to find out this number of squares, you should multiply their number horizontally, by their number vertically:
5 • 3 \u003d 15 cm², and numbers 5 and 3 are sides of the rectangle.
IMPORTANT:In calculations, all measurements must be expressed in the same units of measure, that is, if the length is expressed in decimeters or centimeters, then the height is expressed in decimeters or centimeters. And then the area will be expressed in square units.
Rectangle area - examples of calculation
The area of \u200b\u200bthe rectangle can be calculated by different options. In the tasks, certain data are given and they should be substituted in all the formulas that were studied before that to find the necessary value. Let's look at one of them. If the task is given in the task of one side and the diagonal of the rectangle, then what in this case will be the area of \u200b\u200bthe rectangle? The knowledge of the Pythagoras theorem is useful here.
This theorem is about the sides of a rectangular triangle. It can also be used to find the sides in a rectangle. After all, if two values \u200b\u200bare known, then the third can already be found, knowing the previous formulas of geometry. About the corners now we will not talk, we will first deal with the sides.
Pythagorean theorem It is the simplest equation. It says that the hypotenuse in the square of the triangle (or it is also the longest side of the rectangular triangle), equal to the sum of the squares of the legs. The equation is the simplest and it can be recorded as follows:
b² + a² \u003d c², where to note that c - besides the fact that the hypotenuse, as well as the diagonal of the rectangle, and segments a and B are sides of a rectangle and a coat of a rectangular triangle.
Consider a specific example to understand how to calculate the area of \u200b\u200bthe rectangle, when one side is known, say A \u003d 8 centimeters and diagonal C \u003d 10 centimeters. If the rectangle is divided into two equal rectangular triangles, then you can easily find the Pythagoras theorem, which is equal to the second cattle or side of the figure. And already according to these data you can find the area of \u200b\u200bthe rectangle itself.
So:
- c² \u003d B² + A²
- b² \u003d C² - A²
- b² \u003d 100 - 64
- b² \u003d 36
- b \u003d 6 centimeters
When the sides are known at the rectangle, you can apply the formula for the area of \u200b\u200bthe rectangle to find its size:
S \u003d 6 • 8 \u003d 48 square centimeters.
The example shows that the area can be found in all kinds of methods, the main thing is to know the formulas and properties of previous classes in geometry and skillfully apply them in practice.
Video: Rectangle area - geometry
