How do we calculate the perimeter of polygons?

As long as we are dealing with a shape characterized by straight lines, the perimeter calculation will be performed by adding together all of the side lengths. This is a simple arithmetic operation that does not require any special skills. For example:

The perimeter of a shape with sides of 5, 9, 4, 6 and 7, will be 31. All you need to do is simply add up all of the sides.

Why can such a question be challenging? Owing to the fact that in tests, they don't want to examine you on arithmetic operations like addition, but rather on your proficiency in the properties of specific shapes. Therefore, you need to know the properties of polygons as they are.

Suggested Topics to Practice in Advance

  1. Area
  2. Parallelogram
  3. The area of a parallelogram: what is it and how is it calculated?
  4. Areas of Polygons for 7th Grade
  5. How do we calculate the area of complex shapes?

Practice Perimeter of a Parallelogram

Examples with solutions for Perimeter of a Parallelogram

Exercise #1

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

Step-by-Step Solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

AB=CD=2 AB=CD=2

AD=BC=7 AD=BC=7

Now we can add all the sides together and find the perimeter:

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

Answer

18 cm

Exercise #2

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 #3

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?

1.51.51.5AAABBBCCCDDD9.5

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can state that:

AD=BC=9.5 AD=BC=9.5

AB=CD=1.5 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 1.5+9.5+1.5+9.5=19+3=22

Answer

22 cm

Exercise #4

What is the perimeter of the trapezoid in the figure?

444555999666

Video Solution

Step-by-Step Solution

To find the perimeter we will add all the sides:

4+5+9+6=9+9+6=18+6=24 4+5+9+6=9+9+6=18+6=24

Answer

24

Exercise #5

Look at the triangle below:

666888101010

What is the perimeter of the triangle?

Video Solution

Step-by-Step Solution

The perimeter of the triangle is equal to the sum of all sides together, therefore:

6+8+10=14+10=24 6+8+10=14+10=24

Answer

24

Exercise #6

Given the triangle:

777111111131313

What is its perimeter?

Video Solution

Step-by-Step Solution

The perimeter of a triangle is equal to the sum of all its sides together:

11+7+13=11+20=31 11+7+13=11+20=31

Answer

31

Exercise #7

Look at the trapezoid in the diagram.

101010777121212777

What is its perimeter?

Video Solution

Step-by-Step Solution

In order to calculate the perimeter of the trapezoid we must add together the measurements of all of its sides:

7+10+7+12 =

36

And that's the solution!

Answer

36

Exercise #8

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 #9

Look at the rectangle below:

AAABBBCCCDDD107

Calculate its perimeter.

Video Solution

Step-by-Step Solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

AB=CD=10 AB=CD=10

BC=AD=7 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 10+7+10+7=20+14=34

Answer

34

Exercise #10

666444AAABBBDDDCCC

Calculate the perimeter of the given parallelogram:

Video Solution

Step-by-Step Solution

As is true for a parallelogram every pair of opposite sides are equal:

AB=CD=6,AC=BD=4 AB=CD=6,AC=BD=4

The perimeter of the parallelogram is equal to the sum of all sides together:

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

Answer

20

Exercise #11

101010777AAABBBDDDCCC

Calculate the perimeter of the given parallelogram.

Video Solution

Step-by-Step Solution

As is true for a parallelogram each pair of opposite sides are equal and parallel,

Therefore it is possible to argue that:

AC=BD=7 AC=BD=7

AB=CD=10 AB=CD=10

Now we can calculate the perimeter of the parallelogram by adding together all of its sides:

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

Answer

34

Exercise #12

Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.

777121212AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First we need to remember that pairs of opposite sides in a parallelogram are parallel and equal.

Therefore, AB is parallel to CD and BC is parallel to AD.

From this we can conclude that AB = CD = 7.

Also: BC = AD = 12.

Finally we can calculate the perimeter by adding all the sides together:

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

Answer

38

Exercise #13

Calculate the perimeter of the trapezoid below:

999555121212444

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given side lengths of the trapezoid.
  • Step 2: Use the perimeter formula for a trapezoid, which is the sum of the lengths of its sides.
  • Step 3: Perform the necessary addition to compute the perimeter.

Now, let's work through each step:
Step 1: The trapezoid has side lengths of 99, 55, 1212, and 44.
Step 2: The formula for the perimeter PP of a trapezoid is:
P=side1+side2+side3+side4 P = \text{side}_1 + \text{side}_2 + \text{side}_3 + \text{side}_4
Step 3: Plugging in the values, we compute:
P=9+5+12+4 P = 9 + 5 + 12 + 4
Step 4: Calculating the sum:
P=30 P = 30

Therefore, the perimeter of the trapezoid is 3030.

Answer

30

Exercise #14

Calculate the perimeter of the trapezoid below:

161616161616111151515

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Identify the given side lengths of the trapezoid.
  • Apply the formula for the perimeter of a trapezoid.
  • Perform the addition of all side lengths to calculate the perimeter.

Let's work through each step:

Step 1: Identify the given side lengths. The trapezoid has:

  • Top base: a=16 a = 16
  • Bottom base: b=1 b = 1
  • Non-parallel side: c=15 c = 15
  • Other non-parallel side: d=16 d = 16

Step 2: We'll use the formula for the perimeter of a trapezoid:

P=a+b+c+d P = a + b + c + d

Step 3: Plug in the values and perform the calculation:

P=16+1+15+16 P = 16 + 1 + 15 + 16

P=48 P = 48

Therefore, the perimeter of the trapezoid is 48 48 .

Answer

48

Exercise #15

Calculate the perimeter of the trapezoid below:

101010111111555101010

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:

  • Step 1: Identify the side lengths of the trapezoid:
    Top side =10 = 10 , Bottom side =5 = 5 , Left side =10 = 10 , Right side =11 = 11 .
  • Step 2: Apply the perimeter formula:
    The formula for the perimeter P P of a trapezoid is P=a+b+c+d P = a + b + c + d .
  • Step 3: Perform the calculations:
    Substitute the given lengths into the formula:
    P=10+5+10+11=36 P = 10 + 5 + 10 + 11 = 36 .

Therefore, the perimeter of the trapezoid is 36 36 .

Answer

36

Topics learned in later sections

  1. Perimeter of a Parallelogram
  2. Perimeter