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

For example, if the sides of the rectangle are $A, B, C~and~D$, 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.

Example of calculation of the perimeter of a rectangle

In thisrectangle, $KL$ equals$10$ y$LM$, a$4$. We are asked to obtain the perimeter of the rectangle. As we have already specified, we know that theparallel 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:

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:

$2+2+7+7=18$

Answer:

$18$

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:

$4.8+4.8+12+12=33.6$

Answer:

$33.6 cm$

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.

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=$5$

Answer:

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 $90^o$

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.

Examples with solutions for Perimeter of a Rectangle

Exercise #1

Look at the following rectangle:

Find its perimeter.

Video Solution

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:

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

Answer

28

Exercise #2

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?

Video Solution

Step-by-Step Solution

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

$AB=CD=2$

$AD=BC=7$

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

$2+7+2+7=4+14=18$

Answer

18 cm

Exercise #3

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 #4

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 claim 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

Exercise #5

Look at the rectangle below:

Calculate its perimeter.

Video Solution

Step-by-Step Solution

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

$AB=CD=10$

$BC=AD=7$

Now let's add all the sides together to find the perimeter of the rectangle: