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Dealing with the area of a rhombus

What is the area of a rhombus

When talking about the area of a rhombus, one should have a vivid image and a clear understanding of what this rhombus really is, what kind of geometry figure it is, what properties, characteristics and specificities it has, what distinguishes this kind of geometry figure from others. In terms of geometry, a rhombus (this geometry figure has also other names, such as rhombuses or plural rhombi, diamond, sometimes it is even called equilateral quadrilateral, which is really hard to remember and pronounce), is a kind of geometry figure, which has sides that are all of the same length. This fact is the reason why some student often cannot distinguish rhombus from a square, even though they are quite different. In order to be able to find the area all you need is to know the correct formula. In this article, you will learn the formula of the area of a rhombus, how to use it appropriately and also, you will get acquainted with other interesting facts about this kind of geometry figure that you will find very useful when dealing with a number of assignments on geometry. Therefore, keep reading the article attentively.

As a matter of fact, there are different methods to find the area of a rhombus. It depends on what information is provided in your assignment. In other words, taking into consideration what dimensions and variables you already know you will decide what method will be exactly what you need in order to find the area of a rhombus.

At the same time, it is important to mention before we proceed to learning the area, that every rhombus is also a parallelogram and it is at the same time a kite. However, remember that not every parallelogram can be a rhombus. In case if a rhombus has all the sides of the same length, it is considered to be a square. Having said that, remember that not every rhombus is a square, even though every square is a rhombus.

Now, let us enlighten the definition and the meaning of the term «area» as a whole, not only in the context of dealing with a rhombus. Generally speaking, this is a quantity which serves to express the extent of that or another figure or plane, shape, etc. The only condition that the figure needs to have in order to have an area is to be two-dimensional. In terms of physics and mathematics, a two-dimensional figure is the one that has width and length. In other words, these essential two dimensions are exactly the width and length. Below in the article you will find the description of the basic properties of the rhombus which are essential to know when dealing with assignments requiring to find the area of a rhombus.

Basic properties of a rhombus

What you should know when dealing with a rhombus is that this kind of geometry figure has two diagonals. These two diagonals are meant to connect the opposite vertices one to another. There are also two pairs of parallel sides. An important fact about this figure is that the rhombus is a symmetric shape across every diagonal that is located inside of it. Taking into consideration these facts, all the rhombuses have the following properties, which you should know when calculating the area of a rhombus.

  • The first property of a rhombus is that its angles that are opposite one to another are considered to have the same measure. This property proves that every rhombus is at the same time a parallelogram.
  • The second property of a rhombus is that the two diagonals that are located inside of this kind of geometry figure are perpendicular one to another. This property leads to the fact that all the rhombuses are considered to be also orthodiagonal quadrilaterals.
  • The diagonals that are located inside of a rhombus always bisect the angles that are opposite to them.

If to discuss the first property of a rhombus more precisely, which says that every rhombus is a parallelogram, we should mention that all the properties of the parallelogram are also peculiar to a rhombus. These properties are considered to be the following: the sides of the rhombus that are opposite one to another are also parallel one to another; the two diagonals located inside the rhombus are supposed to bisect one another and all the possible lines that can be drawn through the midpoint are bound to bisect the area.

Now that you are aware of the basic properties of the rhombus you can proceed to learning more precisely the area and how to apply appropriate formula when completing your assignment on geometry. Below, we provided some guidelines describing how to find the area with the help of relevant formula.

Calculating the area of a rhombus

As we have already said, there are several ways to calculate the area of a rhombus. They depend on what information is provided in your assignment, what variables are known and what are yet to find. Therefore, in order to learn how to find the area of a rhombus, read carefully the following guidelines:

  • The first method to find the area of a rhombus is to use the diagonal. When talking about diagonals, one should mean the lines connecting the corners of the rhombus that are located on the opposite sides. The diagonals that are located inside of a rhombus are perpendicular. In addition, they create four right geometry figures (triangles) when intersecting each other.
  • The next step when applying this method will be multiplying the length of the known diagonals. Here, you need to write down the numbers identifying the length of the given diagonals. After that, you will have to multiply them. Remember squaring units, as long as you are dealing with the square units when calculating the area.
  • Your next step is going to be dividing the received result by two. By means of this, you will find the area of the rhombus, which is exactly what you were looking for.
  • Check the correctness of your answer by undertaking the same steps in the opposite order. This will help you make sure that your answer is absolutely correct.
  • Another method to find the area is using the base of the given figure and its height. In order to do this, naturally you will have to find the base and the height at first.
  • In order to find the base and the height of the given rhombus, you can multiply the altitude of the given geometry figure with the length of one of the sides of the rhombus.
  • Your next step is going to be multiplying the base and the height of the given figure. Now that you are aware of the height of the figure, you have to is to multiply the numbers determining the base and the height. By means of this, you will find the area of a rhombus.
  • Write down the final answer and check whether it is correct by following the same guidelines in the opposite order.
  • The last method of calculating the area is using the trigonometry. Here, you need to deal with squaring the length of one of the sides of the rhombus. As long as the rhombus has four sides which are all of the same length, you can choose whatever side you want, it will not matter.
  • After that, you will need to multiply the number that you received when undertaking the previous step by the sine of one of the angles of the rhombus. As a natter of fact, you can choose whatever angle you want, it doesn’t matter.

Calculating the perimeter of a rhombus

As long as you have already learned how to find the area of a rhombus, we recommend you getting familiar with the guidelines explaining how to calculate the perimeter of this kind of geometry figure. It is not a very difficult matter to deal with, just read the following guidelines carefully.

  • At first, you need to ensure that you are going to work with the rhombus. There have to be four sides of the same length and two pairs of opposite angles that are also equal.
  • Make sure that you know and understand the meaning of the perimeter. When talking of perimeter, one should mean the distance around the whole shape of that or another figure. You can calculate the perimeter of any figure just by adding the length of its sides together.
  • You need to find out the length of all the sides of the figure. As long as you are working with a rhombus, all the sides of the figure are of the same length. Therefore, if you know the length of only one side, you can think of it as if you know the length of every side of the given rhombus.
  • In order to find the perimeter, you need to add all the sides of the given figure one to another. Taking into consideration that a perimeter is supposed to be the length of all the sides of the geometry figure, all you have to do is to add the length of four sides together.
  • Apart from adding the sides one to another, you can also multiply the length of one side by four, as long as this is the number of sides of the rhombus.

If you read all these guidelines attentively enough, there will be no problem for you nor when dealing with the area of a rhombus, neither when dealing with calculating the perimeter of the figure. Both of the tasks are easy enough to complete if you know how to apply appropriate formula.

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