Perimeter

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 a triangle!

Calculate the perimeter of the trapezoid according to the following data:

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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 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 2

O is the center of the circle in the diagram.

What is its perimeter?

Question 3

$$ r=7 $$

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

$$ r=6 $$

Calculate the circumference.

Question 2

$$ r=11 $$

Calculate the circumference.

Question 3

Find the perimeter of the parallelogram using the data below.

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

Calculate the perimeter of the following parallelogram:

Question 2

Calculate the perimeter of the following parallelogram:

Question 3

Given the trapezoid:

What is its perimeter?

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

What is the perimeter of the trapezoid in the figure?

Question 2

Look at the trapezoid in the figure.

Calculate its perimeter.

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

Look at the triangle below:

What is the perimeter of the triangle?

Question 2

Given the triangle:

What is its perimeter?

Question 3

Calculate the perimeter of the trapezoid according to the following data:

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

Calculate the perimeter of the trapezoid according to the following data:

Video Solution

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:

List the lengths of the sides: the bases are $10$ and $12$ , and the two non-parallel sides are each $7$ .
Apply the perimeter formula for a trapezoid: $P = a + b + c + d$ .
Substitute the given values into the formula: $P = 10 + 12 + 7 + 7$ .
Calculate the sum: $P = 10 + 12 + 7 + 7 = 36$ .

Therefore, the perimeter of the trapezoid is $36$ .

This matches the correct answer choice from the provided options.

Answer

Exercise #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?

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AD=BC=9.5$

$AB=CD=1.5$

Now we can add all the sides together and find the perimeter:

$1.5+9.5+1.5+9.5=19+3=22$

Answer

22 cm

Examples and exercises with solutions for the perimeter of a trapezoid

Exercise #1

Calculate the perimeter of the trapezoid according to the following data:

Video Solution

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:

List the lengths of the sides: the bases are $10$ and $12$ , and the two non-parallel sides are each $7$ .
Apply the perimeter formula for a trapezoid: $P = a + b + c + d$ .
Substitute the given values into the formula: $P = 10 + 12 + 7 + 7$ .
Calculate the sum: $P = 10 + 12 + 7 + 7 = 36$ .

Therefore, the perimeter of the trapezoid is $36$ .

This matches the correct answer choice from the provided options.

Answer

Exercise #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?

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AD=BC=9.5$

$AB=CD=1.5$

Now we can add all the sides together and find the perimeter:

$1.5+9.5+1.5+9.5=19+3=22$

Answer

22 cm

Examples and exercises with solutions for the perimeter of the triangle

Exercise #1

Calculate the perimeter of the trapezoid according to the following data:

Video Solution

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:

List the lengths of the sides: the bases are $10$ and $12$ , and the two non-parallel sides are each $7$ .
Apply the perimeter formula for a trapezoid: $P = a + b + c + d$ .
Substitute the given values into the formula: $P = 10 + 12 + 7 + 7$ .
Calculate the sum: $P = 10 + 12 + 7 + 7 = 36$ .

Therefore, the perimeter of the trapezoid is $36$ .

This matches the correct answer choice from the provided options.

Answer

Exercise #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?

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AD=BC=9.5$

$AB=CD=1.5$

Now we can add all the sides together and find the perimeter:

$1.5+9.5+1.5+9.5=19+3=22$

Answer

22 cm

Examples and exercises with solutions for the perimeter of the rectangle

Exercise #1

Calculate the perimeter of the trapezoid according to the following data:

Video Solution

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:

List the lengths of the sides: the bases are $10$ and $12$ , and the two non-parallel sides are each $7$ .
Apply the perimeter formula for a trapezoid: $P = a + b + c + d$ .
Substitute the given values into the formula: $P = 10 + 12 + 7 + 7$ .
Calculate the sum: $P = 10 + 12 + 7 + 7 = 36$ .

Therefore, the perimeter of the trapezoid is $36$ .

This matches the correct answer choice from the provided options.

Answer

Exercise #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?

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AD=BC=9.5$

$AB=CD=1.5$

Now we can add all the sides together and find the perimeter:

$1.5+9.5+1.5+9.5=19+3=22$

Answer

22 cm

Do you know what the answer is?

Question 1

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 2

O is the center of the circle in the diagram.

What is its perimeter?

Question 3

$$ r=7 $$

Calculate the circumference.

Start practice

What is the perimeter?

Test yourself on perimeter of a triangle!

Units of Measurement for Perimeter

Perimeter of the Square

Perimeter of the Rectangle

Perimeter of the triangle

Perimeter of a Rhombus

Perimeter of a Parallelogram

Circle Perimeter

Perimeter of the Trapezoid

Perimeter of the deltoid

Perimeter of Composite Figures

What is the difference between perimeter and surface area?

Examples and exercises with solutions for the perimeter of the parallelogram

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Examples and exercises with solutions for the perimeter of a trapezoid

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Examples and exercises with solutions for the perimeter of the triangle

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Examples and exercises with solutions for the perimeter of the rectangle

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

More Questions

Perimeter of a Rectangle

Circumference

Perimeter of a Parallelogram

Perimeter of a Trapezoid

Perimeter of a Triangle