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 A, B, C~y~D , its perimeter will be AB+BC+CD+DA AB + BC + CD + DA . It is customary to indicate the perimeter by the letter P 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.

Image The perimeter of rectangle P=AB + BC + CD + DA

Suggested Topics to Practice in Advance

  1. Area
  2. Rectangle
  3. Calculating the Area of a Rectangle

Practice Perimeter of a Rectangle

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?
4.84.84.8121212AAABBBCCCDDD

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 #2

Look at the following rectangle:

AAABBBCCCDDD95

Find its perimeter.

Video Solution

Step-by-Step Solution

Since in a rectangle all pairs of opposite sides are equal:

AD=BC=5 AD=BC=5

AB=CD=9 AB=CD=9

Now we calculate the perimeter of the rectangle by adding the sides:

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

Answer

28

Exercise #3

Given the following rectangle:

AAABBBCCCDDDEEEFFF4615

What is the perimeter of the rectangle ABCD?

Video Solution

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

Answer

50

Exercise #4

Below is a rectangle composed of two squares.

666AAABBBCCCDDDEEEFFF

What is its perimeter?

Video Solution

Step-by-Step Solution

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

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

AC=AB+BC AC=AB+BC

AB=6+6=12 AB=6+6=12

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

AB=FD=12 AB=FD=12

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

2×AB+2×CD 2\times AB+2\times CD

We replace the data:

2×12+2×6= 2\times12+2\times6=

24+12=36 24+12=36

Answer

36

Exercise #5

Given the following rectangle:

AAABBBCCCDDDEEEFFF710

What is the perimeter of the rectangle ABCD?

Video Solution

Step-by-Step Solution

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!

Answer

It is not possible to know

examples with solutions for perimeter of a rectangle

Exercise #1

Given the following rectangle:

AAABBBCCCDDDEEEFFFGGGHHH7543

What is the perimeter of the rectangle ABCD?

Video Solution

Step-by-Step Solution

According to the data let's consider:

CF=DE=3 CF=DE=3

AE=BF=5 AE=BF=5

Now we can calculate BC:

5+3=8 5+3=8

AD=BC=8 AD=BC=8

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

GB=HC=4 GB=HC=4

DH=AG=7 DH=AG=7

Now we can calculate AB:

7+4=11 7+4=11

AB=DC=11 AB=DC=11

Now we can calculate the perimeter of the rectangle ABCD:

8+8+11+11= 8+8+11+11=

16+22=38 16+22=38

Answer

38

Exercise #2

Rectangle ABCD contains three other rectangles.

Calculate the perimeter of ABCD.

AAABBBCCCDDDGGGHHHEEEFFF675

Video Solution

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.

Answer

Not enough data

Exercise #3

What is the perimeter of the white area according to the data?
444222555222EEEFFFGGGDDDCCCAAABBB

Video Solution

Step-by-Step Solution

Answer

26

Exercise #4

Look at the following rectangle:

AAABBBCCCDDDEEE84

ΔEDC is equilateral.

Calculate the perimeter of the rectangle.

Video Solution

Step-by-Step Solution

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

Answer

24

Exercise #5

Look at the following rectangle:

AAABBBCCCDDD10X+26

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

Video Solution

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=10+6+x+2

20=16+x+2 20=16+x+2

20162=x 20-16-2=x

x=2 x=2

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

Perimeter of the rectangle ABCD:

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

Answer

20

examples with solutions for perimeter of a rectangle

Exercise #1

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

AE = 8

BC = 5

P=24P=24P=24555AAABBBCCCDDDEEEFFF8

What is the area of the parallelogram?

Video Solution

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:

2×8+2X=24 2\times8+2X=24

16+2X=24 16+2X=24

We isolate X:

2X=8 2X=8

and divide by 2:

X=4 X=4

Now we can use the Pythagorean theorem to find EB.

(Pythagoras: A2+B2=C2 A^2+B^2=C^2 )

EB2+42=52 EB^2+4^2=5^2

EB2+16=25 EB^2+16=25

We isolate the variable

EB2=9 EB^2=9

We take the square root of the equation.

EB=3 EB=3

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

AB= AE+EB AB=\text{ AE}+EB

AB=8+3=11 AB=8+3=11

And therefore we will apply the area formula:

11×4=44 11\times4=44

Answer

44

Exercise #2

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?

Video Solution

Step-by-Step Solution

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

42=16 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×x 16=1\times x

x=16 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 1+16+1+16=32+2=34

Answer

34

Exercise #3

Look at the following rectangle:

AAABBBCCCDDDEEE84

ΔAEB is isosceles (AE=EB).

Calculate the perimeter of the rectangle ABCD.

Video Solution

Step-by-Step Solution

Answer

8+163 8+16\sqrt3

Exercise #4

Calculate the perimeter of the rectangle below.

181818222

Video Solution

Answer

40

Exercise #5

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?
222777AAABBBCCCDDD

Video Solution

Answer

18 cm

Topics learned in later sections

  1. Perimeter
  2. Congruent Rectangles