With such a concept as area, 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 will also be characterized by area. Even repairs in an apartment cannot be done without this definition. Therefore, the question of how to find the area of a rectangle arises very often on our life path and is important not only for schoolchildren.
For those who don’t know, a 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 let's 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 value. Most often we are faced with a method of determining the area using width and length.
Take a rectangle with width b and length k. To calculate the area of this rectangle, you need to multiply the width by the length. All this can be represented in the form of a formula that will look like this: S = b * k.
Now consider this method with a specific example. It is necessary to determine the area of the 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 determine the area in other ways, since in many cases neither the length nor the width of the rectangle is known to us. However, there are other known quantities. How to find the area of the rectangle in this case?
- If we know the length of the diagonal and one of the angles that make up the diagonal with either side of the rectangle, then in this case we need to remember the area of the right triangle. Indeed, if you look, the rectangle consists of two equal right triangles. So, back to the determined value. First you need to determine the cosine of the angle. Multiply the resulting value by the length of the diagonal. As a result, we get the length of one of the sides of the rectangle. Similarly, but already using the definition of the sine, you can determine the length of the second side. How to find the area of the rectangle now? Yes, it’s very simple to multiply the obtained values.
In the form of a formula, it will look like this:
S = cos (a) * sin (a) * d2, where d is the diagonal length
- Another way to determine the area of a rectangle is through a circle inscribed in it. It applies if 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, by the formula. We will not prove it. But it looks like this: S = 4 * r2, where r is the radius.
It so 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, then how do you know the area of the rectangle in this case? To do this, you need to make a number of simple calculations. As we know, the opposite sides of the rectangle are equal, therefore, the known length multiplied by two must be subtracted from the perimeter value. Divide the result by two and get the length of the second side. Well, then the standard trick, we multiply both sides and get the area of the rectangle. In the form of a formula, it will look like this:
S = b * (P - 2 * b), where b is the length of the side, P is the perimeter.
As you can see the area of the rectangle can be determined in various ways. It all depends on what quantities are known to us before considering this issue. Of course, the latest calculus methods are practically never found in life, but can be useful for solving many problems at school. Perhaps this article will be useful for solving your problems.