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

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Step-by-step video solution

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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

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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

Given the parallelogram:

Calculate the perimeter of the parallelogram.

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.

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