How to find the area of a rectangle

With such a concept as the square, we have to face in our lives every day. So, for example, when building a house, you need to know it in order to calculate the amount of necessary material. The size of the garden plot will also be characterized by the area. Even repairs in the apartment can not be done without this definition. Therefore, the question of how to find the area of a rectangle on our life path rises very often and is important not only for schoolchildren.

For those who do not know, the rectangle is a flat figure, in which the opposite sides are equal, and the angles are 90 °. To indicate the area in mathematics use the English letter S. It is measured in square units: meters, centimeters and so on.

Now try to give a detailed answer to the question of how to find the area of the rectangle. There are several ways to determine this value. Most often we come across a method of determining the area with the help of width and length.

Take a rectangle with a width b and a length k. To calculate the area of a given rectangle, the width must be multiplied by the length. This can all be represented in the form of a formula that looks like this: S = b * k.

And now consider this method on a concrete example. It is necessary to determine the area of a garden plot with a width of 2 meters and a length of 7 meters.

S = 2 * 7 = 14 m2

In mathematics, especially in the upper grades, it is necessary to determine the area in other ways, since in many cases neither the length nor the width of the rectangle is known to us. At the same time, there are other known quantities. How to find the area of a rectangle in this case?

• If we know the length of the diagonal and one of the angles that makes up the diagonal with any side of the rectangle, then in this case we need to remember the area of the right triangle. After all, if you understand, then the rectangle consists of two equal rectangular triangles. So, back to the determined value. First you need to determine the cosine of the angle. The resulting value is multiplied by the length of the diagonal. As a result, we get the length of one of the sides of the rectangle. Similarly, but with the help of the definition of the sine, you can determine the length of the second side. And how to find the area of the rectangle now? It's very simple, to multiply the values obtained.

In the form of a formula, this will look like this:

S = cos (a) * sin (a) * d2, where d is the length of the diagonal

• Another way to determine the area of a rectangle is through a circle inscribed in it. It is used when the rectangle is a square. To use this method, you need to know the radius of the circle. How to calculate the area of a rectangle in this way? Of course, according to the formula. We will not prove it. And it looks like this: S = 4 * r2, where r is the radius.

It happens that instead of the radius we know the diameter of the inscribed circle. Then the formula will look like this:

S = d2, where d is the diameter.

• If one of the sides and the perimeter is known, how do you know the area of a rectangle in this case? For this, it is necessary to perform a series of simple calculations. As we know, the opposite sides of the rectangle are equal, therefore from the perimeter value it is necessary to subtract a known length, multiplied by two. The result is divided into two and we get the length of the second side. Well, and then the standard method, multiply both sides and get the area of the rectangle. In the form of a formula, this will look like this:

S = b * (P - 2 * b), where b - side length, P - perimeter.

As you can see the area of the rectangle can be determined in various ways. Everything depends on what quantities are known to us before considering this issue. Of course, the last methods of calculating in life are practically not found, but they can be useful for solving many problems in school. Perhaps, and to solve your problems, this article will be useful.