Finding the perimeter of the quadrilateral is an important process in understanding tasks with increased complexity. Despite this, the process is not a lot of work. This article will consider options and examples of finding the perimeter of the quadrangle.
The essence of the perimeter
Perimeter is not only a geometric concept. It is used in life. The ability to find the perimeter uses in the construction business, when repairing apartments, building private houses. You will need to calculate the perimeter of the shape, which will surround your home. If you are aware of how important it is to be able to use the perimeter in different areas of real life activities, then it will be much more interesting to study this topic.
It does not matter with which geometric figure you have a business - a square, a rhombus, triangle or a hexagon. It is important that the perimeter of any figure, regardless of its shape and the number of angles, will be the sum of all sides. To find the perimeter, you need to know the meaning of all sides. If the value of any of the parties is not in the condition of the task, you will need to first find it.
Types of quadrangles
In geometry there are a large number of figures. Any figure having four corners (four sides) is a quadrangle.
Below are the main types of quadrangles, which are found in the books by geometry:
- Square. All sides of this figure are equal. To find the perimeter, it is necessary to add them or multiply the value of one side by 4. The formula is as follows: p \u003d a + a + a + a, p \u003d 4a. P - perimeter and a - side length.
Example: Find the perimeter of the square, if it is known that its side is equal to 6.New and reasoning: we already know that to find the perimeter of the square you need to multiply the value of its side to the quantity. Substitting the values \u200b\u200bin the formula, we obtain: p \u003d 4 × 6 \u003d 24. - Rectangle. The rectangle is such a figure where the parallel sides are equal. It has two lengths and two widths. The length of the figure is denoted by the Latin letter A, the width of the same - Latin letter b. The formula for finding the perimeter of the rectangle will have the following form: p \u003d 2a + 2b. Thus, knowing the width and length we can find the perimeter. It is important to remember that if we are familiar to only the length or only width, it is impossible to find the perimeter.
Example: to find P rectangle if its length \u003d 5, and width \u003d 3. Single: we will substitute the values \u200b\u200bof the parties in the formula: P \u003d 2A + 2B \u003d 2 × 5 + 2 × 3 \u003d 10 + 6 \u003d 16 - Rhombus. Roma, like a square, all sides are equal. It is easy to guess that in relation to the rhop, the same formula is used as the square: p \u003d a + a + a + a, p \u003d 4a. P - perimeter and a - side length.
Example: What value will be equal to the perimeter of rhombus if his side is 7 cm. The presentation: we already know that for finding the perimeter of the rhombus, you must multiply the value of it to the quantity. Substitting the values \u200b\u200bin the formula, we obtain: p \u003d 4 × 7 \u003d 28. - Parallelogram. This figure has the parties that lie against each other (parallel) are equal. Thus, the perimeter finding formula for the parallelogram is identical to the perimeter formula for the rectangle. P \u003d 2a + 2b.
Example: Find the perimeter value, if one side of the parallelogram is 9, and the second one. - Trapeze (Equibilities of trapezium, rectangular trapezium). The measurement can be both swollen and equally, as well as rectangular. In independence, on this, based on the essence of the perimeter, all parties must be folded to find it. The trapezium has the following sides: a small base, a large base, left and right side). The formula will have the following form: p \u003d a + b + c + d, where a and b are the numerical values \u200b\u200bof the bases of the trapezium and C, d - the left and right side.
Example: a small base of the trapezion \u003d 3, large - 5. Left side of the wound 2, right - 4. Find perimeter. Applying the above formula, we obtain: p \u003d 3 + 5 + 2 + 4 \u003d 14
All the same actions will need to be done with an equilibrium and a rectangular trapezium. The only difference is that the left and right side of the trapezion is equal to each other. It is logical that the angles will be identical with the big base. A rectangular trapezium has 1 rectangular angle, which is located in a large base of the figure.
Online calculator
Among other things, you can use an online calculator, which in a few seconds will detect you the perimeter value of any shape. There are many calculators in the network for different figures.
When you go to the calculation page, you will need to enter the length of the parties and then click the calculation button. Online program with special simple algorithms will find the value you need. Despite the existence of such calculation methods, you should not abuse them. You should always be able to independently find all the meanings and remember by heart all the formulas.
No one will provide such computing tricks on the test or examination of such computing tricks. They will not be needed, because all this will not be much labor. Below will be a list of pages for different shapes:
As you could make sure, find the perimeter of the quadrilateral, and indeed any figure is very easy. Well study this topic, it will help you in solving more complex tasks, where the perimeter is only one of the steps towards the correct solution of the geometric problem.
Remember that any material requires consolidation and practical training. Therefore, the resources will be given below, going to which you can hone the skill of solutions to find the perimeter of the quadrangle:
- http://www.myshared.ru/slide/370862/
- https://profmeter.com.ua/communication/learning/course/course7/lesson59/
- https://www.math10.com/ru/zadachi/perimetr/easy/
Read theory, it is also important as a practical solution to the tasks. Combine practice and theory, then any topic will be easy to be given to you.
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