Perimeter of a Parallelogram Practice Problems & Exercises

Master parallelogram perimeter calculations with step-by-step practice problems. Learn the formula P=2(a+b) and solve real examples with solutions.

📚What You'll Master in This Practice Session
  • Apply the perimeter formula P=2(a+b) to solve parallelogram problems
  • Calculate missing side lengths when given perimeter and one side
  • Solve algebraic equations involving parallelogram perimeter with variables
  • Work with parallelograms using centimeters and other measurement units
  • Identify opposite sides in parallelograms and use their equal length property
  • Solve multi-step word problems involving parallelogram perimeter calculations

Understanding Perimeter of a Parallelogram

Complete explanation with examples

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.

A6 - Perimeter of a parallelogram

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 .

Detailed explanation

Practice Perimeter of a Parallelogram

Test your knowledge with 19 quizzes

Given the parallelogram:

141414111111AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

Examples with solutions for Perimeter of a Parallelogram

Step-by-step solutions included
Exercise #1

Calculate the perimeter of the following parallelogram:

101010888

Step-by-Step Solution

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

  • Step 1: Identify the given information
  • Step 2: Apply the appropriate perimeter formula for the parallelogram
  • Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us the lengths of two adjacent sides of the parallelogram: a=10a = 10 and b=8b = 8.
Step 2: We'll use the formula for the perimeter of a parallelogram: P=2(a+b)P = 2(a + b).
Step 3: Plugging in our values, we get:

P=2(10+8)=2×18=36 P = 2(10 + 8) = 2 \times 18 = 36

Therefore, the perimeter of the parallelogram is 3636.

Answer:

36

Video Solution
Exercise #2

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

777121212AAABBBCCCDDD

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

Video Solution
Exercise #3

Given the parallelogram:

888666AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

Step-by-Step Solution

To calculate the perimeter of the parallelogram ABCD, we need the lengths of its two adjacent sides. Given that one side, AB, is 8 units, and recalling that adjacent parallelogram sides will mirror their opposites, AC represents a relevant measurement within the context—but sides not involved with inclination describe standard periphery bounds without adjustments (hence reliance on visually positioned evaluation without contradictions).

Following the perimeter formula for parallelograms:

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

In our shape, let’s define:

  • a=8 a = 8 (Length of side AB or its opposite estimation feature equated)
  • b=6 b = 6 (Instinctive reconfirmation according to positive iteration; i.e., default parameter for spatial definition)

Plugging these values into our formula, we get:

P=2(8+6) P = 2(8 + 6) P=2(14) P = 2(14) P=28 P = 28

Therefore, the perimeter of the parallelogram is 28 28 units.

Answer:

28

Video Solution
Exercise #4

Calculate the perimeter of the following parallelogram:

333111

Step-by-Step Solution

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

  • Step 1: Identify the base and side of the parallelogram from the diagram.
  • Step 2: Use the perimeter formula for a parallelogram.
  • Step 3: Substitute the values into the formula to find the perimeter.

Now, let's work through each step:
Step 1: From the diagram, the base of the parallelogram is given as 3 3 units (top side). Despite the lack of explicit vertical length values, the common approach is to assume symmetrical side lengths—both the base and the side given symmetrically leads us to a second side, typically directly inferred. However, since all clear interpretation points to utilizing 1 and horizontal 3, we verify with associated edge matching.
Step 2: Use the formula for the perimeter of the parallelogram: P=2×(base+side) P = 2 \times (\text{base} + \text{side}) .
Step 3: Substitute the given values into the formula: P=2×(3+1) P = 2 \times (3 + 1) .
Calculating this gives us: P=2×4=8 P = 2 \times 4 = 8 .

Therefore, the solution to the problem is P=8 P = 8 .

Answer:

8

Video Solution
Exercise #5

Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

Step-by-Step Solution

To find the perimeter of the parallelogram, we follow these steps:

  • Step 1: Identify the given side lengths from the diagram: AB=4 AB = 4 units and AD=2 AD = 2 units.
  • Step 2: Use the perimeter formula for a parallelogram, which is P=2(a+b) P = 2(a + b) .
  • Step 3: Substituting the given values into the formula: a=4 a = 4 and b=2 b = 2 .

Proceeding with the calculation:

P=2(4+2)=2×6=12 P = 2(4 + 2) = 2 \times 6 = 12 .

Therefore, the perimeter of the parallelogram is 12 units.

Answer:

12

Video Solution

Frequently Asked Questions

What is the formula for the perimeter of a parallelogram?

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The perimeter of a parallelogram is P = 2(a + b) or P = 2a + 2b, where 'a' and 'b' are the lengths of two adjacent sides. Since opposite sides in a parallelogram are equal, you only need to know two adjacent side lengths to calculate the perimeter.

How do you find the perimeter of a parallelogram with sides 5cm and 8cm?

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Using the formula P = 2(a + b), substitute the values: P = 2(5 + 8) = 2(13) = 26cm. You can also calculate it as P = 5 + 5 + 8 + 8 = 26cm since opposite sides are equal in a parallelogram.

How do you find a missing side length when given the perimeter?

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Use the perimeter formula and solve for the unknown side. For example, if P = 20cm and one side is 6cm, then 20 = 2(6 + b), so 20 = 12 + 2b, therefore 2b = 8, and b = 4cm.

What property of parallelograms helps calculate perimeter easily?

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The key property is that opposite sides of a parallelogram are equal in length. This means you only need to measure two adjacent sides instead of all four sides to calculate the perimeter.

Can you solve parallelogram perimeter problems with variables?

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Yes, you can solve algebraic problems involving parallelogram perimeter. Steps include: 1) Write the perimeter formula P = 2(a + b), 2) Substitute known values and variables, 3) Solve the resulting equation for the unknown variable, 4) Check your answer by substituting back into the original equation.

What are common mistakes when finding parallelogram perimeter?

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Common errors include: adding all four sides instead of using the formula when only two sides are given, forgetting that opposite sides are equal, mixing up which sides are adjacent versus opposite, and arithmetic errors when solving algebraic equations.

How is parallelogram perimeter different from rectangle perimeter?

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Both use the same formula P = 2(a + b) since rectangles are special types of parallelograms. However, rectangles have right angles while general parallelograms have opposite angles equal but not necessarily 90 degrees.

What units are typically used for parallelogram perimeter problems?

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Perimeter is measured in linear units such as: centimeters (cm), meters (m), inches (in), feet (ft), or any other length unit. The answer will always be in the same units as the given side lengths, representing the total distance around the parallelogram.

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