Parallelogram ABCD: Finding the Total Perimeter with Known Side Lengths

Q: Why do I multiply by 2 in the perimeter formula?

A parallelogram has four sides, but opposite sides are equal. So if two adjacent sides are 10 cm and 8 cm, the other two sides are also 10 cm and 8 cm. Instead of adding 10 + 8 + 10 + 8, we can use the shortcut: $ 2 \times (10 + 8) = 36 $.

Q: How do I know which sides are opposite to each other?

In parallelogram ABCD, sides AB and CD are opposite (they don't share a vertex), and sides BC and DA are opposite. From the diagram, AB = 10 cm, so CD = 10 cm. Similarly, BC = 8 cm, so DA = 8 cm.

Q: What if the diagram only shows one side length?

You need at least two adjacent side lengths to find the perimeter of a parallelogram. If only one side is given, you don't have enough information unless it's specified that the parallelogram is actually a rectangle or rhombus.

Q: Is this the same as finding the perimeter of a rectangle?

Yes! A rectangle is a special type of parallelogram where all angles are 90°. The perimeter formula is exactly the same: $ P = 2 \times (\text{length} + \text{width}) $.

Parallelogram Perimeter with Two Side Lengths

Given the parallelogram ABCD calculate its perimeter

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of the parallelogram

00:03 Opposite sides are equal in a parallelogram

00:17 The perimeter of the parallelogram equals the sum of its sides

00:24 Let's substitute appropriate values according to the given data, and solve to find the perimeter

00:37 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the parallelogram ABCD calculate its perimeter

Step-by-step solution

To find the perimeter of parallelogram ABCD, we begin by identifying the lengths of its sides:

Side AB is given as $10$ cm.
Side BC is given as $8$ cm.

In a parallelogram, opposite sides are equal in length. Therefore, we also know:

Side CD is $10$ cm (since it is opposite to AB).
Side DA is $8$ cm (since it is opposite to BC).

The formula for the perimeter $P$ of a parallelogram is:

$P = 2 \times (\text{length}_1 + \text{length}_2)$

Substituting the known values into the formula, we have:

$P = 2 \times (10 + 8)$

$P = 2 \times 18$

$P = 36 \, \text{cm}$

Thus, the perimeter of parallelogram ABCD is $36$ cm.

The correct answer is $\textbf{36 cm}$ , which corresponds to choice 3.

Final Answer

36 cm

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of a parallelogram are equal in length
Formula: $P = 2 \times (\text{side}_1 + \text{side}_2)$ where sides are 10 and 8
Check: All four sides should sum to your answer: 10 + 8 + 10 + 8 = 36 ✓

Common Mistakes

Avoid these frequent errors

Adding only the two given side lengths
Don't just add 10 + 8 = 18 cm! This ignores the other two sides of the parallelogram and gives half the actual perimeter. Always remember that a parallelogram has four sides, with opposite sides being equal, so multiply by 2.

Practice Quiz

Test your knowledge with interactive questions

Find the perimeter of the parallelogram using the data below.

FAQ

Everything you need to know about this question

Why do I multiply by 2 in the perimeter formula?

A parallelogram has four sides, but opposite sides are equal. So if two adjacent sides are 10 cm and 8 cm, the other two sides are also 10 cm and 8 cm. Instead of adding 10 + 8 + 10 + 8, we can use the shortcut: $2 \times (10 + 8) = 36$ .

How do I know which sides are opposite to each other?

In parallelogram ABCD, sides AB and CD are opposite (they don't share a vertex), and sides BC and DA are opposite. From the diagram, AB = 10 cm, so CD = 10 cm. Similarly, BC = 8 cm, so DA = 8 cm.

What if the diagram only shows one side length?

You need at least two adjacent side lengths to find the perimeter of a parallelogram. If only one side is given, you don't have enough information unless it's specified that the parallelogram is actually a rectangle or rhombus.

Is this the same as finding the perimeter of a rectangle?

Yes! A rectangle is a special type of parallelogram where all angles are 90°. The perimeter formula is exactly the same: $P = 2 \times (\text{length} + \text{width})$ .

Can I just memorize that the answer is always double the sum?

That's a good pattern to remember! For any parallelogram, the perimeter equals 2 times the sum of two adjacent sides. But make sure you understand why this works - it's because opposite sides are equal.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime