The perimeter indicates the distance we will walk if we start from a certain point, complete a full lap, and return exactly to the starting point. For example, if we are asked what the perimeter of the waist is, we will take a tape measure and measure the perimeter from a certain point until completing a full lap and returning to the same point from which we started the measurement. It works exactly the same way in mathematics. The perimeter of any shape is the distance from a specific point back to it after having completely surrounded it. If this is our figure:
Its perimeter will be the distance we cover if we travel along its line from a certain point, and return to it after making a full lap. Imagine that you are surrounding the figure:
The perimeter is measured in units of mm, cm, or meters, according to what the question states. Generally, most figures are given in units of cm. We can convert the different units of measure in the following way: 1 cm = 10 mm 1 meter = 100 cm
Now we will learn to calculate the perimeter of the most known figures. Are we ready? How is the perimeter calculated in general? All the lengths of the edges (or sides) of the figure are added together. The sum of all the edges is the perimeter.
Perimeter of the Square
a -> Side of the square In the square, all sides are equal, therefore, its perimeter will be 4 times the side a. We will multiply the side of the square by 4.
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Let's add up the sides of the rectangle. The opposite sides are equal.
More information about the Perimeter of the rectangle
Perimeter of the triangle
Let's add up all the sides of the triangle. In an isosceles triangle it is enough to know the length of the base and one of the two equal sides. In an equilateral triangle it is enough to know the length of one side.
More information about the Perimeter of the triangle
The key to calculating the perimeter of these figures is to add up absolutely all the sides without forgetting any of them. Start on one side, follow the entire round and stop when you reach the same side from which you started.
What is the difference between perimeter and surface area?
The perimeter is measured in two-dimensional figures that do not have volume, for example, a rectangle
In contrast, the surface area is measured in three-dimensional figures that do have volume, for example, a cylinder or cube.
Examples and exercises with solutions for the perimeter of the parallelogram
examples.example_title
Given the parallelogram:
Calculate the perimeter of the parallelogram.
examples.explanation_title
As in a parallelogram every pair of opposite sides are equal:
AB=CD=6,AC=BD=4
The perimeter of the parallelogram is equal to the sum of all sides together:
4+4+6+6=8+12=20
examples.solution_title
20
examples.example_title
Given the parallelogram:
Calculate the perimeter of the parallelogram.
examples.explanation_title
As in a parallelogram each pair of opposite sides are equal and parallel,
It is possible to argue that:
AC=BD=7
AB=CD=10
Now we can calculate the perimeter of the parallelogram by adding all its sides:
10+10+7+7=20+14=34
examples.solution_title
34
Examples and exercises with solutions for the perimeter of a trapezoid
examples.example_title
What is the perimeter of the trapezoid in the figure?
examples.explanation_title
To find the perimeter we will add all the sides:
4+5+9+6=9+9+6=18+6=24
examples.solution_title
24
examples.example_title
Look at the trapezoid in the figure.
The long base is 1.5 times longer than the short base.
Find the perimeter of the trapezoid.
examples.explanation_title
First, we calculate the long base from the existing data:
Multiply the short base by 1.5:
5×1.5=7.5
Now we will add up all the sides to find the perimeter:
2+5+3+7.5=7+3+7.5=10+7.5=17.5
examples.solution_title
17.5
Examples and exercises with solutions for the perimeter of the triangle
examples.example_title
Look at the triangle below:
What is the perimeter of the triangle?
examples.explanation_title
The perimeter of the triangle is equal to the sum of all sides together, therefore:
6+8+10=14+10=24
examples.solution_title
24
examples.example_title
Given the triangle:
What is its perimeter?
examples.explanation_title
The perimeter of a triangle is equal to the sum of all its sides together:
11+7+13=11+20=31
examples.solution_title
31
Examples and exercises with solutions for the perimeter of the rectangle
examples.example_title
Look at the rectangle below.
Side AB is 4.8 cm long and side AD has a length of 12 cm.
What is the perimeter of the rectangle?
examples.explanation_title
In the drawing, we have a rectangle, although it is not placed in its standard form and is slightly rotated, but this does not affect that it is a rectangle, and it still has all the properties of a rectangle.
The perimeter of a rectangle is the sum of all its sides, that is, to find the perimeter of the rectangle we will have to add the lengths of all the sides. We also know that in a rectangle the opposite sides are equal. Therefore, we can use the existing sides to complete the missing lengths.
4.8+4.8+12+12 = 33.6 cm
examples.solution_title
33.6 cm
examples.example_title
Look at the following rectangle:
Find its perimeter.
examples.explanation_title
Since in a rectangle all pairs of opposite sides are equal:
AD=BC=5
AB=CD=9
Now we calculate the perimeter of the rectangle by adding the sides:
