Perimeter of a Rectangle - Examples, Exercises and Solutions

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?

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:

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

18 cm

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?

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:

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

22 cm

Look at the following rectangle:

Find its perimeter.

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

Look at the rectangle below:

Calculate its perimeter.

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:

$10+7+10+7=20+14=34$

34

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?

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

Below is a rectangle composed of two squares.

What is its perimeter?

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

Given the square,

What is its perimeter?

Since in a square all sides are equal to each other, all sides are equal to 8 cm

Now we can calculate the perimeter:

$8\times4=32$

32

What is the perimeter of the given rectangle ABCD?

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

We can therefore calculate for the rectangle ABCD that BC=6+4=10

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

Next we calculate the perimeter of the rectangle by adding together all of the sides:

DC=AB=15

Hence the perimeter of the rectangle ABCD is equal to:

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

50

What is the perimeter of the given rectangle ABCD?

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

The left quadrilateral, AEFD, has a known side - AD

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!

It is not possible to know

Given the following rectangle:

What is the perimeter of the rectangle ABCD?

Based on the given data, we know that:

$AD=BC=5$

$AB=AE+EB$

$AB=7+EB$

We are missing data to determine the length of AB, and therefore we cannot calculate the perimeter of the rectangle

It is not possible to know

What is the perimeter of the white area according to the data?

26

Rectangle ABCD contains three other rectangles.

Calculate the perimeter of ABCD.

Let's look at rectangle EBHF where we are given:

EF=BH=5

FH=EB=6

From this we can calculate AB:

7+6=13

Now we have a pair of sides in rectangle ABCD:

AB=DC=13

We know that EF=BH=AG=5

We therefore do not have enough additional data to calculate the sides AD and BC.

Not enough data

What is the perimeter of the given rectangle ABCD?

According to the data let's consider:

$CF=DE=3$

$AE=BF=5$

Now we can calculate BC:

$5+3=8$

$AD=BC=8$

Next we pay attention to any additional information and it seems that:

$GB=HC=4$

$DH=AG=7$

Hence we can calculate AB:

$7+4=11$

$AB=DC=11$

Lastly we can calculate the perimeter of the rectangle ABCD:

$8+8+11+11=$

$16+22=38$

38

Given the following rectangle:

What is the perimeter of the rectangle ABCD?

According to the given data:

$JC=HB=3$

$DI=AG=3$

$FD=EC=3$

$BE=AF=4$

$GH=JI=6$

Now we can calculate sides AB and DC

$3+6+3=9+3=12$

And also sides AD and BC

$4+3=7$

Now we can calculate the perimeter of rectangle ABCD:

$12+7+12+7=24+14=38$

38

Look at the following rectangle:

ΔEDC is equilateral.

Calculate the perimeter of the rectangle.

A rectangle has two pairs of equal opposite sides.

That is:

BC=AD=4

AB=DC

In an equilateral triangle, all sides are equal, therefore:
EC=CD=DE

We know that EC=8, so:

EC=CD=DE=8

We know that:

AB=DC

Therefore:

AB=DC=8

Remember that the perimeter of a rectangle is equal to the sum of all its sides, therefore:

AB+BC+DC+AD

We substitute in all its known sides:

8+4+8+4=

24

24