# Perimeter of a Rectangle - Examples, Exercises and Solutions

## 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.

## 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!

It is not possible to know

### Exercise #6

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

26

### Exercise #7

Rectangle ABCD contains three other rectangles.

Calculate the perimeter of ABCD.

### Step-by-Step Solution

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

### Exercise #8

Given the following rectangle:

What is the perimeter of the rectangle ABCD?

### Step-by-Step Solution

According to the data let's consider:

$CF=DE=3$

$AE=BF=5$

Now we can calculate BC:

$5+3=8$

$AD=BC=8$

We pay attention to the additional data we know and it seems that:

$GB=HC=4$

$DH=AG=7$

Now we can calculate AB:

$7+4=11$

$AB=DC=11$

Now we can calculate the perimeter of the rectangle ABCD:

$8+8+11+11=$

$16+22=38$

38

### Exercise #9

Look at the following rectangle:

ΔEDC is equilateral.

Calculate the perimeter of the rectangle.

### Step-by-Step Solution

A rectangle has two pairs of equal opposite sides.

That is:

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:

We substitute in all its known sides:

8+4+8+4=

24

24

### Exercise #10

The rectangle in the diagram is composed of of three smaller rectangles.

Calculate x given that GDEF has a perimeter of 44.

### Step-by-Step Solution

Let's calculate the perimeter of rectangle GDEF using the given data:

$10x-8+10x-8+5x+5x=44$

We'll group similar terms:

$30x-16=44$

$30x=44+16$

$30x=60$

$x=2$

2

### Exercise #11

Look at the following rectangle:

Given that the perimeter of the triangle BCD is 20, what is the perimeter of the rectangle ABCD?

### Step-by-Step Solution

Given that the perimeter of triangle BCD is 20

Therefore, we can place the existing data and calculate:

$20=10+6+x+2$

$20=16+x+2$

$20-16-2=x$

$x=2$

Now we can calculate the BC side: 2+2=4

Perimeter of the rectangle ABCD:

$6+6+4+4=12+8=20$

20

### Exercise #12

The parallelogram ABCD contains the rectangle AEFC inside it, which has a perimeter of 24.

AE = 8

BC = 5

What is the area of the parallelogram?

### Step-by-Step Solution

In the first step, we must find the length of EC, which we will identify with an X.

We know that the perimeter of a rectangle is the sum of all its sides (AE+EC+CF+FA),

Since in a rectangle the opposite sides are equal, the formula can also be written like this: 2AE=2EC.

We replace the known data:

$2\times8+2X=24$

$16+2X=24$

We isolate X:

$2X=8$

and divide by 2:

$X=4$

Now we can use the Pythagorean theorem to find EB.

(Pythagoras: $A^2+B^2=C^2$)

$EB^2+4^2=5^2$

$EB^2+16=25$

We isolate the variable

$EB^2=9$

We take the square root of the equation.

$EB=3$

The area of a parallelogram is the height multiplied by the side to which the height descends, that is$AB\times EC$.

$AB=\text{ AE}+EB$

$AB=8+3=11$

And therefore we will apply the area formula:

$11\times4=44$

44

### Exercise #13

The area of the square whose side length is 4 cm is
equal to the area of the rectangle whose length of one of its sides is 1 cm.

What is the perimeter of the rectangle?

### Step-by-Step Solution

After squaring all sides, we can calculate the area as follows:

$4^2=16$

Since we are given that the area of the square equals the area of the rectangle , we will write an equation with an unknown since we are only given one side length of the parallelogram:

$16=1\times x$

$x=16$

In other words, we now know that the length and width of the rectangle are 16 and 1, and we can calculate the perimeter of the rectangle as follows:

$1+16+1+16=32+2=34$

34

### Exercise #14

Look at the following rectangle:

ΔAEB is isosceles (AE=EB).

Calculate the perimeter of the rectangle ABCD.

### Step-by-Step Solution

$8+16\sqrt3$

### Exercise #15

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?