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:
The equal edges are marked with the letters a and b. Let's note the perimeter of the parallelogram: P=a+a+b+b=2a+2B=2(a+b)
Now let's do it in a clear way.
The formula to calculate the perimeter of a parallelogram is: P=2a+2b
or 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, 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:
P=3+4+3+4=14
Solution: The perimeter of the parallelogram is 14cm.
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)
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
Solution: The perimeter of the parallelogram is 16cm.
Example 3
Given that the perimeter of the parallelogram is 16cm. Likewise, we know that the length of one of the sides is 6cm. How long is the other side?
First, let's draw a parallelogram ABCD
Given P=16
Let's mark the lengths of the sides with the letters a and b. We know that a=6 Let's use the formula we just learned: P=2a+2b
Let's place the data in the formula and we will get:
P=2×6+2×b=16
12+2b=16
2b=4
b=2
That is, we have found that the length of the other side is 2cm.
We can verify our result by doing the following calculation: a+a+b+b=6+6+2+2=16
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
BC=DA=4
P=12×2+4×2=32
The perimeter of the parallelogram is 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 ofTutorelayou will find a variety of articles about mathematics.
Perimeter of a Parallelogram Exercises
Exercise 1:
Statement
Given the parallelogram ABCD
Given that:
AB=4
AC=x−2
The perimeter of the parallelogram is equal to 10
Find x
Solution
We use the formula for calculating the perimeter of the parallelogram
P=2×AB+2×AC=10
We replace the existing data in the formula
P=2×4+2×(x−2)=10
We solve accordingly
P=8+2x−4=10
P=4+2x=10
We move the 4 to the right section and keep the corresponding sign
P=2x=10−4
P=2x=6
We divide by: 2
P=x=3
Answer
3
Exercise 2:
Statement
Given the parallelogram ABCD
Given that:
AB=6
AC=x
The perimeter of the parallelogram is equal to 20
Find x
Solution
We use the formula for calculating the perimeter of the parallelogram
P=2×AB+2×AC=20
We replace the existing data in the formula
P=2×6+2×x=20
We solve accordingly
P=12+2x=20
We move the 12 to the right section and keep the corresponding sign
P=2x=20−12
P=2x=8
We divide by: 2
P=x=4
Answer
4
Exercise 3:
Statement
Given the parallelogram ABCD
Given that:
AB=8
AC=x+2
The perimeter of the parallelogram is equal to 30
Find x
Solution
We use the formula for calculating the perimeter of the parallelogram
P=2×AB+2×AC=30
We replace the existing data in the formula
P=2×8+2×(x+2)=30)
We solve accordingly
P=16+2x+4=30
P=20+2x=30
We move the 20 to the right section and keep the corresponding sign
P=2x=30−20
P=2x=10
We divide by: 2
P=x=5
Answer
5
Exercise 4:
Statement
Given the parallelogram ABCD
Given that:
AB=10
AC=x
The perimeter of the parallelogram is equal to 30
Find x
Solution
We use the formula for calculating the perimeter of the parallelogram
P=2×AB+2×AC=30
We replace the existing data in the formula
P=2×10+2×x=30
We solve accordingly
P=20+2x=30
We move the 20 to the right section and keep the corresponding sign
P=2x=30−20
P=2x=10
We divide by: 2
P=x=5
Solution
5
Exercise 5:
Statement
Given the parallelogram ABCD
Given that:
AB=7
AC=0.5x
The perimeter of the parallelogram 21
Find AC
Solution
We use the formula for calculating the perimeter of the parallelogram
P=2×AB+2×AC=21
We replace the existing data in the formula
P=2×7+2×0.5x=21
We solve accordingly
P=14+1x=21
We move the 14 to the right section and keep the appropriate sign