How to get the AREA of a rectangle with the PERIMETER

From a teacher we are happy to bring a new lesson in which we are going to learn how to find the area of ​​a rectangle with the perimeter and knowing one of the sides. To do this, we will remember what a rectangle is and what its characteristics are, and then see how to calculate the area with its typical formula. From there, we will see how to calculate the area with the perimeter and we will do exercises, of which you can find the solution at the end of the post.

Index

1. What is a rectangle?
2. Area and perimeter of a rectangle
3. How to find the area of ​​a rectangle with the perimeter? With example
4. Exercise on taking the area of ​​a rectangle with the perimeter
5. Solution

Before explaining how to find the area of ​​a rectangle with the perimeter, it is important that we understand the mathematical term so that we can better follow this lesson.

To define what is a rectangle clearly, we could say that it is, in geometry, the flat polygon that has four sides

The area is the calculation that allows the discovery of the space occupies a figure, in this case, a rectangle. As we always mention when we talk about the area, we must remember that the area must always be accompanied by the units squared, that is, if we receive the data in meters, the area will be in meters squared. In addition, it is necessary that the units of the statement coincide, that is, if one side is given in meters and the other in centimeters, we must unify it to the same unit in order to calculate the area.

Once all this is understood, we can calculate the area of ​​a rectangle. The formula is:

• Area = b x h
• Where b = base; h = height.

Therefore, the formula is simple, you simply have to multiply one of the sides by the other that is not your parallel, that is, multiply the base by the height, taking into account that the units of measurement are the themselves.

On the other hand, the perimeter is calculated by adding the length of the four sides, although as two to two are equal, we can also say that we can calculate the perimeter by multiplying the base by two and adding the height multiplied by two as well. The formula is:

1. Perimeter = 2 x b + 2 x h,
2. Where b = base; h = height.

For calculate the area of ​​a rectangle with the perimeter, we have to know two things: the first, the perimeter; the second, the base or the height.

Let's see it from a example:

A rectangle that has a perimeter of 28 square meters and one side, the base, is 8 meters, what is its area? Let's solve it step by step:

1. First, we substitute in the perimeter formula all the data that we know, that is, we go from having P = 2 x b + 2 x h, to having 28 = 2 x 8 + 2 x h.
2. We solve that equation: 28 = 16 + 2 x h -> 28 - 16 = 2 x h -> 12 = 2 x h -> 12/2 = h -> h = 6.
3. We already have that the height is 6 meters, so now we substitute that in the formula for the area, so that we will go from having A = b x h, to having A = 8 x 6 -> A = 48 meters.

We are going to check if you have understood what is explained in this lesson, so, so that you can practice, we propose the following exercise:

Find the area of ​​the following rectangle:

• It has a perimeter of 20 centimeters and a side of 5 centimeters.

The solution to the proposed exercise is the following:

• P = 2 x b + 2 x h ->
• 20 = 2 x 5 + 2 x h ->
• 20 = 10 + 2 x h ->
• 20 - 10 = 2 x h ->
• 10 = 2 x h ->
• 10/2 = 2 x h ->
• h = 5 centimeters

So the area will be 5 x 5, so the area is 25 square centimeters.

If you are interested in learning more about geometry, you can continue browsing our website, where you will find lessons and videos to understand everything you want to know. We encourage you to do so!

Image: Matemáticas18.com

If you want to read more articles similar to How to find the area of ​​a rectangle with the perimeter, we recommend that you enter our category of Geometry.