Perimeter of a Parallelogram

🏆Practice perimeter of a parallelogram

The formula to calculate the perimeter of a parallelogram

You have probably already realized that it is not necessary to calculate all the edge lengths to find the perimeter.

Let's look at the parallelogram ABCD ABCD :

The equal edges are marked with the letters a a and b b . Let's note the perimeter of the parallelogram:
P=a+a+b+b=2a+2B=2(a+b) P=a+a+b+b=2a+2B=2\left(a+b\right)

Now let's do it in a clear way.

The formula to calculate the perimeter of a parallelogram is:
P=2a+2b P=2a+2b

or
P=2(a+b) P=2(a+b)

There is no difference between both formulas, we can use whichever we want.

The perimeter of the parallelogram is equal to the sum of its four edges (or sides). As we know, in a parallelogram there are two pairs of opposite edges of equal length, therefore, knowing the length of two adjacent sides is enough to calculate the perimeter of the figure.

For example, if we observe the parallelogram ABCD ABCD , given the length of its sides in cm:

As we have mentioned, the perimeter is the sum of the length of its sides. Consequently, we will note:

A1 - The perimeter of the parallelogram = P=3+4+3+4=14

P=3+4+3+4=14 P=3+4+3+4=14

Solution: The perimeter of the parallelogram is 14cm 14cm .

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Test yourself on perimeter of a parallelogram!

einstein

Calculate the perimeter of the parallelogram ABCD.

CD is parallel to AB.

777121212AAABBBCCCDDD

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Let's remember that the parallelogram has a very important property:

In a parallelogram, there are two pairs of opposite edges of equal length.

Therefore, knowing the length of two adjacent sides is enough to calculate the perimeter of the figure.

Examples

Example 1

Given the parallelogram ABCD ABCD :

A2 - Example Given the parallelogram ABCD

Given that:
CD=3 CD=3

AD=5 AD=5

All lengths are given in centimeters

Calculate the perimeter of the parallelogram.

Solution:

As we know that in a parallelogram the length of each pair of opposite sides is equal, we can conclude that:

AB=CD=3 AB=CD=3 [object Object]AD=BC=5 AD=BC=5

Now we can add the lengths of the sides and find the perimeter. We will write it as follows:
P=AB+CD+AD+BC=3+3+5+5=16 P=AB+CD+AD+BC=3+3+5+5=16

That is:
The perimeter of the parallelogram is 16cm 16cm .


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Example 2

A3 - Given the parallelogram ABCD BC=6 DC=2

Given the parallelogram ABCD ABCD .  
BC=6 BC=6

DC=2 DC=2

The lengths of the sides are shown in cm. Calculate the perimeter of the parallelogram.

We will notice that it is not necessary to calculate the length of each side (or edges). Let's use the formula we just learned to calculate the perimeter of the parallelogram:

P=2(a+b) P=2\left(a+b\right)

Knowing that a and b are the dimensions of the two adjacent sides.
Let's place the given numbers and we will obtain:
P=2(a+b)=2(2+6)=2×8=16 P=2\left(a+b\right)=2\left(2+6\right)=2\times8=16

Solution:
The perimeter of the parallelogram is 16cm 16cm .


Example 3

Given that the perimeter of the parallelogram is 16cm 16cm . Likewise, we know that the length of one of the sides is 6cm 6cm . How long is the other side?

First, let's draw a parallelogram ABCD ABCD

A4 - Given the parallelogram ABCD  P=16 a=6 P=2a+2b

Given P=16 P=16

Let's mark the lengths of the sides with the letters a a and b b . We know that a=6 a=6
Let's use the formula we just learned:
P=2a+2b P=2a+2b

Let's place the data in the formula and we will get:

P=2×6+2×b=16 P=2\times6+2\times b=16

12+2b=16 12+2b=16

2b=4 2b=4

b=2 b=2

That is, we have found that the length of the other side is 2cm 2cm .

We can verify our result by doing the following calculation:
a+a+b+b=6+6+2+2=16 a+a+b+b=6+6+2+2=16

Therefore, our result is correct.


Do you know what the answer is?

Example 4

Given the parallelogram ABCD ABCD in the diagram.

A5 - Given the parallelogram ABCD  AB=12 BC=4

The following is true: AB=12 AB=12 and
BC=4 BC=4

Based on the given data, we are asked to find the perimeter of the parallelogram.
As we have already mentioned, opposite sides of a parallelogram are equal, therefore: 
AB=CD=12 AB=CD=12

AB=CD=12 AB=CD=12

BC=DA=4 BC=DA=4

P=12×2+4×2=32 P=12\times2+4\times2=32

The perimeter of the parallelogram is 32cm 32cm


If you are interested in learning more about the perimeters of geometric shapes, you can enter one of the following articles:

Parallel lines

Parallelogram - Checking the parallelogram

The area of the parallelogram: what is it and how is it calculated?

The perimeter of the rectangle

Rectangles with equivalent area and perimeter

How is the perimeter of a triangle calculated?

How is the perimeter of a trapezoid calculated?

The perimeter of the circumference

Ways to identify parallelograms

Rotational symmetry in parallelograms

On the website of Tutorela you will find a variety of articles about mathematics.


Perimeter of a Parallelogram Exercises

Exercise 1:

Statement

Given the parallelogram ABCD ABCD

Given that:

AB=4 AB=4

AC=x2 AC=x-2

The perimeter of the parallelogram is equal to 10 10

Find x x

Given the parallelogram ABCD

Solution

We use the formula for calculating the perimeter of the parallelogram

P=2×AB+2×AC=10 P=2\times AB+2\times AC=10

We replace the existing data in the formula

P=2×4+2×(x2)=10 P=2\times4+2\times\left(x-2\right)=10

We solve accordingly

P=8+2x4=10 P=8+2x-4=10

P=4+2x=10 P=4+2x=10

We move the 4 4 to the right section and keep the corresponding sign

P=2x=104 P=2x=10-4

P=2x=6 P=2x=6

We divide by: 2 2

P=x=3 P=x=3

Answer

3 3


Exercise 2:

Statement

Given the parallelogram ABCD ABCD

Given that:

AB=6 AB=6

AC=x AC=x

The perimeter of the parallelogram is equal to 20 20

Find x x

parallelogram ABCD We use the formula for calculating the perimeter of the parallelogram

Solution

We use the formula for calculating the perimeter of the parallelogram

P=2×AB+2×AC=20 P=2\times AB+2\times AC=20

We replace the existing data in the formula

P=2×6+2×x=20 P=2\times6+2\times x=20

We solve accordingly

P=12+2x=20 P=12+2x=20

We move the 12 12 to the right section and keep the corresponding sign

P=2x=2012 P=2x=20-12

P=2x=8 P=2x=8

We divide by: 2 2

P=x=4 P=x=4

Answer

4 4


Exercise 3:

Statement

Given the parallelogram ABCD ABCD

Given that:

AB=8 AB=8

AC=x+2 AC=x+2

The perimeter of the parallelogram is equal to 30 30

Find x x

The perimeter of the parallelogram is equal to 30

Solution

We use the formula for calculating the perimeter of the parallelogram

P=2×AB+2×AC=30 P=2\times AB+2\times AC=30

We replace the existing data in the formula

P=2×8+2×(x+2)=30) P=2\times8+2\times\left(x+2)=30\right)

We solve accordingly

P=16+2x+4=30 P=16+2x+4=30

P=20+2x=30 P=20+2x=30

We move the 20 20 to the right section and keep the corresponding sign

P=2x=3020 P=2x=30-20

P=2x=10 P=2x=10

We divide by: 2 2

P=x=5 P=x=5

Answer

5 5


Exercise 4:

Statement

Given the parallelogram ABCD ABCD

Given that:

AB=10 AB=10

AC=x AC=x

The perimeter of the parallelogram is equal to 30 30

Find x x

Exercise 4 - Given the parallelogram ABCD

Solution

We use the formula for calculating the perimeter of the parallelogram

P=2×AB+2×AC=30 P=2\times AB+2\times AC=30

We replace the existing data in the formula

P=2×10+2×x=30 P=2\times10+2\times x=30

We solve accordingly

P=20+2x=30 P=20+2x=30

We move the 20 20 to the right section and keep the corresponding sign

P=2x=3020 P=2x=30-20

P=2x=10 P=2x=10

We divide by: 2 2

P=x=5 P=x=5

Solution

5 5


Exercise 5:

Statement

Given the parallelogram ABCD ABCD

Given that:

AB=7 AB=7

AC=0.5x AC=0.5x

The perimeter of the parallelogram 21 21

Find AC AC

The perimeter of the parallelogram 21

Solution

We use the formula for calculating the perimeter of the parallelogram

P=2×AB+2×AC=21 P=2\times AB+2\times AC=21

We replace the existing data in the formula

P=2×7+2×0.5x=21 P=2\times7+2\times0.5x=21

We solve accordingly

P=14+1x=21 P=14+1x=21

We move the 14 14 to the right section and keep the appropriate sign

P=1x=2114 P=1x=21-14

P=1x=7 P=1x=7

We divide by: 1 1

P=x=7 P=x=7

We calculate AC AC

7×0.5=3.5 7\times0.5=3.5

Answer

3.5 3.5


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