Calculate Parallelogram Perimeter: 8.1 and 8 Unit Side Lengths

Q: Why don't I need to add all four sides separately?

In a parallelogram, opposite sides are equal! So instead of adding 8.1 + 8 + 8.1 + 8, you can use the formula $ P = 2(a + b) $ where you multiply by 2 to account for both pairs.

Q: How do I know which sides are adjacent?

Adjacent sides are sides that share a corner. In any parallelogram, you only need one pair of adjacent sides since the opposite sides are always equal in length.

Q: Can I use this formula for rectangles and squares too?

Yes! Rectangles and squares are special types of parallelograms, so the formula $ P = 2(a + b) $ works perfectly for them as well.

Parallelogram Perimeter with Decimal Side Lengths

Calculate the perimeter of the following parallelogram:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's calculate the perimeter of the parallelogram.

00:12 Remember, in a parallelogram, opposite sides are equal, so this will help us.

00:21 To find the perimeter, we simply add up all the sides. Easy, right?

00:40 And that's how we find the perimeter of a parallelogram!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the perimeter of the following parallelogram:

Step-by-step solution

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

Step 1: Identify the given side lengths of the parallelogram.
Step 2: Use the formula for the perimeter of a parallelogram.
Step 3: Plug the side lengths into the formula and calculate.

Now, let's work through the steps:

Step 1: The given side lengths are 8.1 and 8.
Step 2: The formula for the perimeter $P$ of a parallelogram with sides $a$ and $b$ is: $P = 2(a + b)$ .
Step 3: Substitute the given side lengths into the formula:

$P = 2(8.1 + 8)$

Calculate inside the parentheses first:

$P = 2 \times 16.1$

Then multiply:

$P = 32.2$

Therefore, the perimeter of the given parallelogram is $32.2$ .

Final Answer

32.2

Key Points to Remember

Essential concepts to master this topic

Rule: Parallelogram perimeter equals 2 times sum of adjacent sides
Technique: Use formula P = 2(a + b) where a = 8.1 and b = 8
Check: Sum adjacent sides first: 8.1 + 8 = 16.1, then multiply: 2 × 16.1 = 32.2 ✓

Common Mistakes

Avoid these frequent errors

Adding all four sides instead of using the formula
Don't add 8.1 + 8 + 8.1 + 8 individually = 32.2 but takes longer and risks arithmetic errors! This wastes time and increases chances of mistakes. Always use the formula P = 2(a + b) to calculate efficiently.

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 don't I need to add all four sides separately?

In a parallelogram, opposite sides are equal! So instead of adding 8.1 + 8 + 8.1 + 8, you can use the formula $P = 2(a + b)$ where you multiply by 2 to account for both pairs.

What if the side lengths were given as fractions?

The same formula works! Just be careful with your arithmetic when adding fractions. Convert to common denominators first, then add, and finally multiply by 2.

How do I know which sides are adjacent?

Adjacent sides are sides that share a corner. In any parallelogram, you only need one pair of adjacent sides since the opposite sides are always equal in length.

Can I use this formula for rectangles and squares too?

Yes! Rectangles and squares are special types of parallelograms, so the formula $P = 2(a + b)$ works perfectly for them as well.

What if I get a different answer when adding manually?

Double-check your decimal arithmetic! Make sure you're adding 8.1 + 8 = 16.1 correctly, then multiplying by 2. Common errors happen when handling the decimal point.

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