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.
Side AB is 2 cm long and side BC has a length of 7 cm.
What is the perimeter of the rectangle?
Incorrect
Correct Answer:
18 cm
Question 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?
Incorrect
Correct Answer:
33.6 cm
Question 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?
Incorrect
Correct Answer:
22 cm
Question 4
What is the perimeter of the trapezoid in the figure?
Incorrect
Correct Answer:
24
Question 5
Look at the triangle below:
What is the perimeter of the triangle?
Incorrect
Correct Answer:
24
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?
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
AD=BC=7
Now we can add all the sides together and find the perimeter:
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?
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?
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
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
Answer
22 cm
Exercise #4
What is the perimeter of the trapezoid in the figure?
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
Answer
24
Exercise #5
Look at the triangle below:
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
Answer
24
Question 1
Given the triangle:
What is its perimeter?
Incorrect
Correct Answer:
31
Question 2
Look at the trapezoid in the diagram.
What is its perimeter?
Incorrect
Correct Answer:
36
Question 3
Look at the following rectangle:
Find its perimeter.
Incorrect
Correct Answer:
28
Question 4
Look at the rectangle below:
Calculate its perimeter.
Incorrect
Correct Answer:
34
Question 5
Calculate the perimeter of the given parallelogram:
Incorrect
Correct Answer:
20
Exercise #6
Given the triangle:
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
Answer
31
Exercise #7
Look at the trapezoid in the diagram.
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:
Find its perimeter.
Video Solution
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
Answer
28
Exercise #9
Look at the rectangle below:
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
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
Answer
34
Exercise #10
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
The perimeter of the parallelogram is equal to the sum of all sides together:
4+4+6+6=8+12=20
Answer
20
Question 1
Calculate the perimeter of the given parallelogram.
Incorrect
Correct Answer:
34
Question 2
Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.
Incorrect
Correct Answer:
38
Question 3
Calculate the perimeter of the trapezoid below:
Incorrect
Correct Answer:
30
Question 4
Calculate the perimeter of the trapezoid below:
Incorrect
Correct Answer:
48
Question 5
Calculate the perimeter of the trapezoid below:
Incorrect
Correct Answer:
36
Exercise #11
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
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
Answer
34
Exercise #12
Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.
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
Answer
38
Exercise #13
Calculate the perimeter of the trapezoid below:
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 9, 5, 12, and 4.
Step 2: The formula for the perimeter P of a trapezoid is: P=side1+side2+side3+side4
Step 3: Plugging in the values, we compute: P=9+5+12+4
Step 4: Calculating the sum: P=30
Therefore, the perimeter of the trapezoid is 30.
Answer
30
Exercise #14
Calculate the perimeter of the trapezoid below:
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
Bottom base: b=1
Non-parallel side: c=15
Other non-parallel side: d=16
Step 2: We'll use the formula for the perimeter of a trapezoid:
P=a+b+c+d
Step 3: Plug in the values and perform the calculation:
P=16+1+15+16
P=48
Therefore, the perimeter of the trapezoid is 48.
Answer
48
Exercise #15
Calculate the perimeter of the trapezoid below:
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, Bottom side =5, Left side =10, Right side =11.
Step 2: Apply the perimeter formula:
The formula for the perimeter P of a trapezoid is P=a+b+c+d.
Step 3: Perform the calculations:
Substitute the given lengths into the formula: P=10+5+10+11=36.