Learning how to find the area of a rectangle
To know how to find the area of a rectangle is a common requirement that all the students have to satisfy when studying in the secondary school, because this issue is an integral part of the educational program within the studies of mathematics. As a matter of fact, rectangle is the geometry figure that is met most often among all the rest of figures. It is quite simple, with simple properties and characteristics which are not really difficult to learn. As a rule, students complete assignments requiring the knowledge of how to find the area of a rectangle without facing huge difficulties. On the fact whether you are capable or not to cope with finding the area of the rectangle, whether you and understand how to find the area of a rectangle or not, depends your further success in the studies of mathematics, particularly geometry, since this is one of the essentials of geometry, the basis that gives the understanding of other more complicated and difficult issues. In this article, you will learn how to find the area of a rectangle by means of different methods and formulas. In addition, you will learn interesting and useful facts about geometry as a branch of mathematics as a whole, which will be helpful when dealing within within your studies in the high school.
Rectangles are the basic shapes in geometry. A rectangle is a kind of geometry figure that has four sides, and four angles. The two sides of a rectangle are of the similar length and the other two sides of the rectangle are of the equal width. In other words, a rectangle has two pairs of sides, and each pair consists of two sides of equal size. Apart from it, all the four internal angles located between the sides of this geometry figure are right. The easiest and common way to find the area of a rectangle is simply use the dimensions of the two sides of the figure and multiply one with another. If you have an assignment requiring the knowledge how to find the area of a rectangle, read attentively the guidelines provided below and follow them when dealing with this assignment.
- As for the start, you need to make sure that you understand such geometry figure as a rectangle. It’s main specificity is that it is quadrilateral. This fact means that the figure has four sides, and the sides located one in front of another are equal. Therefore, the two sides of a rectangle represent its length and are equal and the other two sides represent the width of the rectangle and they are also equal.
- Keep in mind that all the existing squares are rectangles at the same time, although not all the existing rectangles can be squares, which are characterized by the fact that all their sides are equal and any side of a square can represent width or length. In terms of the task where you have find the area of a rectangle, you can treat all the squares like they are rectangles, although don’t treat all the rectangles like they are squares.
- You have to learn and understand the equation that is needed when looking for the area of a rectangle. This equation shows how to find the area of a rectangle in a simple manner: to multiply the number indicating the length of the rectangle by the number indicating its width.
- Proceed to finding the length of the given rectangle. As a rule, assignments on geometry provide such dimensions, but if this data is not provided, you will have to turn to the help of a ruler.
- Once you got the length of the rectangle found, you need to search for the width of it. Here, you can apply the same method as it is described in the previous step.
- When measuring the height of the rectangle and its width, keep in mind that you need to measure not the sides that are located in front of each other but those between which there is a right angle.
- Write down the dimensions that you have found next to each other. If you rectangle is a square, the dimensions have to be equal. But in case if you are dealing with a rectangle that is not a square, you will have different length and width.
- Now that you have all the dimensions required for finding the area of the rectangle and you know how to find the area of a rectangle, you need to use them appropriately.
- Write down the formula how to find the area of a rectangle right after the dimensions. The formula has to look like this: a=lxw. The a indicates the area of the rectangle, the l indicates the length of the rectangle and the w serves to indicate the width of the figure.
- For example, if the length of the given rectangle is 3 and its width is 5, you will have to multiply 3 by five and you will get the are of the figure: 3×5= 15. in this case, the area of the rectangle is 15.
- Once you have found the answer to your assignment on geometry, you need to write it down in square units (since this is how you need to write down the answer every time when you deal with the are of that or another geometry figure).
- There are two methods to write down the answer: according to the first method, you can write the answer like this: 15 cm^2. On the other hand, you can write the answer like this: 15 cm.sq. In both of cases such manner of writing the answer will mean the same.
How to find the area of a rectangle using the diagonal
Apart from the formula how to find the area of a rectangle that is already provided in the article, there are also other methods to find the area of a rectangle. Usually students turn to other methods in case if they don’t know the dimensions of the width and length of the given rectangle or if they know one one dimension, which is also not enough to find the area of a rectangle by using such formula. Therefore, another way to deal with this task is to use the dimensions of only one side of the rectangle and the diagonal. Read the guidelines provided below attentively and follow them when completing your assignment on geometry.
- The starting point will be to learn and understand the Pythagorean theorem. This is a theorem that is used when working with triangles. It is a formula that shows how to find the unknown side of triangle in case if the other two sides are already known.
- Consider using the Pythagorean theorem in order to find the hypothenuse of the triangle located within the given rectangle (keep in mind that hypothenuse is considered to be the longest side of the triangle) or the length of the figure that touches the right angle. Also, you can apply this theorem to finding the width of the triangle.
- Keep in mind that a rectangle consists of four right angles. This means that the diagonal that comes through the overall shape of the rectangle creates a right triangle, which allows you to use the formula of the Pythagorean theorem.
- Write down the formula of the Pythagorean theorem, which has to look like this: a^2 + b^2 = c^2. Here, the symbols a and b are indicating the sides of the geometry figure and the letter c serves to indicate its longest side.
- No that you have all the needed data you have to apply the Pythagorean theorem to your problem. For example, in case if you have a rectangle with a diagonal of 20 cm and with one side of 5 cm, you need to use these dimensions as those indicating two sides of a right triangle, one of which is the longest one.
- Your next step will be to enter the dimensions that you are aware of into the formula of the Pythagorean theorem. Therefore, your formula will look like this: 5×5 + b = 20×20, where b is going to be the third side of the right triangle and the side of the give rectangle at the same time.
- As a result, you will get the needed number indicating the side of the rectangle that you were looking for.
- Now that you have all the necessary information for getting the area of the rectangle, you need to apply it to the formula that has already been provided in the beginning of the article: multiply the width of the given rectangle by its length.
- Just like in the previous example, you will have to state the answer to your question in square units.
What you should also know about rectangles
Apart from being aware how to find the area of a rectangle and being able to use the needed formulas appropriately, it is also important to possess some theoretical background in regard to such geometry figure as rectangle. While it is one of the basic shapes in geometry, it has its own history, referring to the ancient times when people only started taking an interest in sciences. The rectangle was an object of research in Euclidean geometry. This is a specific mathematical system, which was created by an outstanding mathematician Euclid, who was the author of the first book on geometry in the history of the world. He called his book Elements and included there a wide range of geometry theorems, axioms, etc. As a matter of fact, this remarkable mathematician appeared to be the first man in the world who managed to demonstrate how geometry was related to a number of other sciences and how it could be used within the logical system. His book starts with the explanation of elementary geometry, which is today taught in secondary schools far and wide across the world. Apart from plane geometry, in the book most of attention was paid to the researches of three dimensions, referring to the solid geometry. What today is called like algebra and the theory of numbers was also explained in the book of Euclid.
It has to be mentioned that for a long time, more than a thousand years, the book written by Euclid considered to be absolutely unnecessary, it was almost ignored by the mathematicians who argued that all the information provided in the book is so obvious and elementary that there was no need to use it, since the science of mathematics was a far more complex issue and required deeper insight. However, not so long ago it has been recognized that the book Elements is a genuine contribution to the world of science, because it gave birth to all the discoveries in the area of geometry that we all know and use in our lives today.
Generally speaking, the book Elements was a grounded research that provided a clear systematization of the essentials of geometry. Even though we tend to speak of Elements as if it is a single book, the truth is that there are thirteen books in the series of Elementary as a whole. They are divided into groups in accordance with the complexity of the study. From the very beginning, the books are dedicated to the studies of elementary geometry and beginning from the eleventh book Euclid provided the works concerning solid geometry. Therefore, all the books enlighten all the major issues concerning geometry on different levels.
Learning of every discipline begins with elementary issues, like knowing how to find the area of a rectangle. Later within your studies you will face more and more complicated issues and all of them will require total understanding of everything that you are dealing with now. For this reason, it is very important to pay enough of attention to the study of geometry beginning from now in order to be successful in it later. Besides, geometry, unlike some other disciplines, may appear to be really useful in your everyday life. If you take it seriously now, you will ease your life in the future. In case if you need help with your homework, don’t hesitate to turn to the help of people who have a lot of experience in the area of your studies and are always ready to provide you with all the necessary assistance.
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