with this notion, as the area, we have to face in their daily lives.For example, when building a house it is necessary to know in order to calculate the amount of material required.The size of a garden site also will feature area.Even repairs in the apartment can not be done without this definition.So the question is how to find the area of a rectangle, on our life's journey, and often gets is important not only for students.
For those who do not know, a rectangle - a plane figure whose opposite sides are equal and the angles are 90 °.To identify areas in mathematics using 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 a rectangle.There are several ways to determine this quantity.Most often we are faced with the method of determining the area using the width and length.
Take a rectangle with width b and length k.To calculate the area of a rectangle is necessary to multiply the width by the length.This can all be represented as a formula that looks like this: S = b * k.
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 high school, we have to identify the area in other ways, as in many cases, neither the length nor the width of the rectangle is unknown to us.However, 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 constituting a diagonal from any side of the rectangle, in this case, you need to remember about the area of a right triangle.After all, if you look, the box is divided into two equal right triangles.So back to the defined value.First we need to determine the cosine of the angle.The resulting value is multiplied by the length of the diagonal.As a result, we obtain the length of one side of the rectangle.Similarly, but using a sine determination can determine the length of the second side.But how to find the area of a rectangle is now?It's very easy to multiply the values obtained.
as the formula would look like this:
S = cos (a) * sin (a) * d2, where the length of the diagonal d-
- Another method for determining the area of a rectangle - through inscribed in a circle.It is used when the rectangle is a square.To use this method, you must know the radius of the circle.How to calculate the area of a rectangle in such a way?Of course, according to the formula.To prove it, we will not.And it looks so: S = 4 * r2, where r is the radius.
happens that instead we know the radius of the inscribed circle diameter.Then the formula would look like this:
S = d2, where d - diameter.
- If you know one of the parties and the perimeter, then how to find the area of a rectangle in this case?To do this, you must make a number of simple calculations.As we know, the opposite sides of the rectangle are equal, so the value of the perimeter subtract known length multiplied by two.The obtained result is divided by two and obtain the length of the second side.Oh, and then a standard technique, multiply both sides and get the area of a rectangle.In a formula would look like this:
S = b * (P - 2 * b), where b - side length, P - perimeter.
As we can see the area of a rectangle can be defined in various ways.It all depends on what we know of the value before consideration of the issue.Of course, the latest calculation methods in life almost never occur, but can be useful for solving many problems in school.Perhaps, for your application, this article will be useful.
