Perimeter | Tutorela

What is the perimeter?

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:

Detailed explanation

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Test yourself on perimeter of the triangle!

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

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Units of Measurement for Perimeter

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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Test your knowledge

Question 1

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?

Question 2

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

Question 3

$$ r=11 $$

Calculate the circumference.

Perimeter of the Rectangle

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

Do you know what the answer is?

Question 1

$$ r=7 $$

Calculate the circumference.

Question 2

$$ r=2 $$

Calculate the circumference.

Question 3

$$ r=6 $$

Calculate the circumference.

Perimeter of a Rhombus

$a$ -> side of the rhombus
In the rhombus all sides are equal, therefore, its perimeter will be 4 times the side a.

Perimeter of a Parallelogram

Let's add up the sides of the parallelogram. The opposite sides are equal.

More information about the Perimeter of a parallelogram

Check your understanding

Question 1

A circle has a radius of 3 cm.

What is its perimeter?

Question 2

O is the center of the circle in the diagram.

What is its perimeter?

Question 3

O is the center of the circle in the figure below.

What is its circumference?

Circle Perimeter

$r$ –> Radius of the circumference
Pi $π$ will be calculated as the number –> $3.14$

Let's multiply Pi –> $3.14$ by the radius by $2$

More information about the Circle's perimeter

Perimeter of the Trapezoid

Let's add up all the sides of the trapezoid

More information about the Perimeter of the trapezoid

Do you think you will be able to solve it?

Question 1

O is the center of the circle.

AB = 15

Is it possible to work out its circumference?

Question 2

Look at the circle in the figure.

Is it possible to calculate its circumference?

Question 3

What is the perimeter of the trapezoid in the figure?

Perimeter of the deltoid

In the deltoid, the 2 adjacent sides are equal.

Perimeter of Composite Figures

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.

Let's see an example:

The area is:
$4+4+4+5+2+8+2+3=32$

Test your knowledge

Question 1

What is the perimeter of the trapezoid in the figure?

Question 2

Look at the trapezoid in the figure.

Calculate its perimeter.

Question 3

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

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

The perimeter in two-dimensional figures

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

Exercise #1

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?

Video Solution

Step-by-Step Solution

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

Answer

33.6 cm

Exercise #2

O is the center of the circle in the figure below.

What is its circumference?

Video Solution

Step-by-Step Solution

We use the formula: $P=2\pi r$

We replace the data in the formula: $P=2\times8\pi$

$P=16\pi$

Answer

$16\pi$ cm

Examples and exercises with solutions for the perimeter of a trapezoid

Exercise #1

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?

Video Solution

Step-by-Step Solution

Answer

33.6 cm

Exercise #2

O is the center of the circle in the figure below.

What is its circumference?

Video Solution

Step-by-Step Solution

We use the formula: $P=2\pi r$

We replace the data in the formula: $P=2\times8\pi$

$P=16\pi$

Answer

$16\pi$ cm

Examples and exercises with solutions for the perimeter of the triangle

Exercise #1

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?

Video Solution

Step-by-Step Solution

Answer

33.6 cm

Exercise #2

O is the center of the circle in the figure below.

What is its circumference?

Video Solution

Step-by-Step Solution

We use the formula: $P=2\pi r$

We replace the data in the formula: $P=2\times8\pi$

$P=16\pi$

Answer

$16\pi$ cm

Examples and exercises with solutions for the perimeter of the rectangle

Exercise #1

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?

Video Solution

Step-by-Step Solution

Answer

33.6 cm

Exercise #2

O is the center of the circle in the figure below.

What is its circumference?

Video Solution

Step-by-Step Solution

We use the formula: $P=2\pi r$

We replace the data in the formula: $P=2\times8\pi$

$P=16\pi$

Answer

$16\pi$ cm

Do you know what the answer is?

Question 1

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?

Question 2

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

Question 3

$$ r=11 $$

Calculate the circumference.

Start practice