# The perimeter of the rectangle

🏆Practice perimeter of a rectangle

## The perimeter of the rectangle is the sum of the length of all its sides.

For example, if the sides of the rectangle are $A, B, C~y~D$, its perimeter will be $AB + BC + CD + DA$. It is customary to indicate the perimeter by the letter $P$.

Important to remember!

Rectangles have two pairs of opposite, parallel and equal sides. Therefore, it is enough to know the length of two coincident sides to calculate their perimeter.

## Test yourself on perimeter of a rectangle!

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?

## Example of calculation of the perimeter of a rectangle

In this rectangle, $KL$ equals $10$ y $LM$, a $4$. We are asked to obtain the perimeter of the rectangle. As we have already specified, we know that the parallel sides are identical and, thus: $KL=MN=10$, while $LM=NK=4$. Thus: $P=10+10+4+4=28$

This can also be expressed as follows: $P=10×2+4×2=28$

If you are interested in this article, you may be interested in the following articles:

Rectangle

Area of a rectangle

Rectangles of Equivalent Area and Perimeter

From a quadrilateral to a rectangle

In Tutorela' s blog you will find a variety of interesting articles about mathematics.

## Exercises of the perimeter of a rectangle

### Exercise 1

Question:

What is the perimeter each of the two rectangles according to the data?

Solution:

To calculate the area of the rectangle we use the calculus formula.

The perimeter of the rectangle is equal to the sum of all its sides.

We divide the answer by 2:

The perimeter of the rectangle $ABCD$ (large) will be.$AB+BC+CD+DA$

The perimeter of the large rectangle is $4+5+4+5+4+4=26$

The perimeter of the rectangle $EFGD$ (small) will be $EF+FG+GD+DE$

The perimeter of the small rectangle is $2+2+4+4=12$

The perimeter of the rectangle $ABCD$ is $26$ cm.

The perimeter of the rectangle $EFGD$ is $12$ cm

Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today

### Exercise 2

Given the rectangle that the side $AB$ is equal to $2$ cm and the side $BC$ is equal to $7$ cm.

Question:

What is the value of the perimeter of the rectangle?

Solution:

To solve for the answer we will put the data into a formula for calculating the area of a rectangle which is basically calculating all the sides of the rectangle:

Since the parallel sides of the rectangle have the same length, it can be said that:

$AB=2$

$DC=2$

$BC=7$

$AD=7$

Therefore the calculation of the perimeter is:

$2+2+7+7=18$

$18$

### Exercise 3

Given a rectangle with a side $AB$ of $4.8$ cm long and a side $AD$ of $12$ cm long.

Question:

What is the perimeter of the rectangle?

Solution:

To solve for the answer we will put the data into the formula for calculating the area of the rectangle which is basically calculating all the sides of the rectangle:

Since the parallel sides of the rectangle have the same length, it can be said that:

$AB=4.8$

$DC=4.8$

$BC=12$

$AD=12$

Therefore the calculation of the perimeter of the rectangle is:

$4.8+4.8+12+12=33.6$

$33.6 cm$

Do you know what the answer is?

### Exercise 4

Given the rectangle in the figure:

The perimeter of the rectangle is $30$.

Question:

How much is its area?

Solution:

Pay attention, in this question we are asked to calculate the area of the rectangle.

The data we have are:

one side (sides also serve as height in a rectangle). $=5$

Together they are equal to $10$

Step $2$, we know that the perimeter of the rectangle is 30 so we can conclude that the perimeter of the two sides of the base is $20$ and since they are equal to each other (the properties of the rectangle) each is equal to $10$.

To solve this question we must put the data into a formula to calculate the rectangular area:

The formula to calculate a rectangular area is: Height multiplied by the base.

Put the data we have into the formula:

Base = $10$

Height=$5$

Area of the rectangle is equal to $50$ cm².

## Review questions

### What is a rectangle?

It is a geometric figure with 4 sides where it consists of two pairs of parallel opposite straight lines, its angles measure $90^o$

### What is the perimeter of a rectangle?

The perimeter of any geometric figure is to calculate the sum of all its sides, in the case of the rectangle is to add its 4 sides, i.e. the entire contour of the geometric figure, it is worth mentioning that the rectangle has two pairs of equal sides.

### What is the formula for finding the perimeter of a rectangle?

In order to calculate the perimeter of a rectangle, we must calculate the sum of all its sides, let it be the following rectangle given with base and height

Then the formula for the rectangle to calculate the perimeter is:

$P=b+h+b+h$

Ó

$P=2b+2h$

Since as we said the rectangle has two pairs of equal sides.

Do you think you will be able to solve it?

### What is the formula for finding the area of a rectangle?

The formula for the rectangle is as follows:

$A=Base\times altura$

$A=b\times a$

### How do you get the area and perimeter of a rectangle, example?

Given the following rectangle calculate perimeter and area:

According to these data, and as we know that a rectangle its opposite sides measure the same then we have the following:

$AB=6\operatorname{cm}$

$BC=9\operatorname{cm}$

$CD=6\operatorname{cm}$

$DA=9\operatorname{cm}$

According to the perimeter formula we add up all its sides.

$P=AB+BC+CD+DA$

$P=6\operatorname{cm}+9\operatorname{cm}+6\operatorname{cm}+9\operatorname{cm}=30\operatorname{cm}$

Now let's calculate the area, using the area formula we have that

$A=Base\times altura$

So:

$A=9\operatorname{cm}\times6\operatorname{cm}=54cm^2$

$P=30 {cm}$

$A=54 {cm^2}$

## examples with solutions for perimeter of a 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?

### 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

33.6 cm

### Exercise #2

Look at the following rectangle:

Find its perimeter.

### Step-by-Step Solution

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:

$5+5+9+9=10+18=28$

28

### Exercise #3

Below is a rectangle composed of two squares.

What is its perimeter?

### Step-by-Step Solution

In a square, all sides are equal. Therefore:
$AB+BC+CD+DE+EF+FA=6$

Thus, we find out what the side AC is equal to:

$AC=AB+BC$

$AB=6+6=12$

In a rectangle, we know that the opposite sides are equal to each other, therefore:

$AB=FD=12$

Therefore, the formula for the perimeter of the rectangle will look like this:

$2\times AB+2\times CD$

We replace the data:

$2\times12+2\times6=$

$24+12=36$

36

### Exercise #4

Given the following rectangle:

What is the perimeter of the rectangle ABCD?

### Step-by-Step Solution

Given that in the smaller rectangle ED=CF=4 (each pair of opposite sides in the rectangle are equal)

Now we can calculate in the rectangle ABCD that BC=6+4=10

Now we can state in the rectangle ABCD that BC=AD=10

Calculate the perimeter of the rectangle by adding all the sides:

DC=AB=15

The perimeter of the rectangle ABCD is equal to:

$10+10+15+15=20+30=50$

50

### Exercise #5

Given the following rectangle:

What is the perimeter of the rectangle ABCD?

### Step-by-Step Solution

In the statement, we have two rectangles that are connected by a common side,

The right quadrilateral, EBCF, also has only one known side: FC

In the question, we are asked for the perimeter of the rectangle ABCD,

For this, we need its sides, and since the opposite sides in a rectangle are equal, we need at least two adjacent sides.

We are given the side AD, but the side DC is only partially given.

We have no way of finding the missing part: DF, so we have no way of answering the question.

This is the solution!