Calculate Parallelogram Perimeter: Using Side Lengths 8 and 3

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

Because a parallelogram has two pairs of equal opposite sides! If one side is 8 units and the adjacent side is 3 units, then you have sides measuring: 8, 3, 8, 3. That's why we use $ P = 2(a + b) $.

Q: How do I know which measurements are the adjacent sides?

Adjacent sides are next to each other, not across from each other. In the diagram, look for two sides that meet at a corner - those are your adjacent sides with lengths 8 and 3.

Q: What if I'm given different side measurements?

The method stays the same! Just identify the two different side lengths (adjacent sides), then use $ P = 2(a + b) $. Remember: opposite sides are always equal in parallelograms.

Q: Can I just add all four sides individually?

Yes, but it's more work! You'd get 8 + 3 + 8 + 3 = 22. The formula $ P = 2(a + b) $ is faster and less prone to addition errors.

Q: What's the difference between a parallelogram and a rectangle?

A rectangle is a special type of parallelogram where all angles are 90°. Both have opposite sides equal, so the perimeter formula $ P = 2(a + b) $ works for both shapes!

Parallelogram Perimeter with Adjacent Side Measurements

Given the parallelogram:

Calculate the perimeter of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's find the perimeter of the parallelogram.

00:06 Remember, opposite sides in a parallelogram are equal.

00:12 We'll substitute the length of one side here.

00:22 The opposite side is equal too, just like before.

00:27 Now, let's fill in the value for the other side.

00:37 To find the perimeter, add up all sides together.

00:57 Let's plug in the values and calculate the total perimeter.

01:10 And that's how we solve this problem! Well done.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the parallelogram:

Calculate the perimeter of the parallelogram.

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Identify the lengths of the adjacent sides of the parallelogram.
Step 2: Use the formula for the perimeter of a parallelogram, $P = 2(a + b)$ .
Step 3: Plug in the known values and calculate the perimeter.

Now, let's work through each step:

Step 1: From the diagram, we have two adjacent sides of the parallelogram: $a = 8$ units and $b = 3$ units.

Step 2: The formula for the perimeter of a parallelogram is given by $P = 2(a + b)$ .

Step 3: Substitute the values for $a$ and $b$ into the formula:

$P = 2(8 + 3) = 2 \times 11 = 22$ .

Therefore, the perimeter of the parallelogram is $22$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are always equal in length
Formula: Perimeter = 2(a + b) where a=8 and b=3
Verification: Check that all four sides add up: 8+3+8+3=22 ✓

Common Mistakes

Avoid these frequent errors

Adding only the given side lengths without doubling
Don't just calculate 8 + 3 = 11! This only gives you two sides, not the full perimeter. A parallelogram has four sides total. Always use P = 2(a + b) to account for both pairs of equal opposite sides.

Practice Quiz

Test your knowledge with interactive questions

Given the parallelogram of the figure

What is your area?

FAQ

Everything you need to know about this question

Why do I multiply by 2 in the perimeter formula?

Because a parallelogram has two pairs of equal opposite sides! If one side is 8 units and the adjacent side is 3 units, then you have sides measuring: 8, 3, 8, 3. That's why we use $P = 2(a + b)$ .

How do I know which measurements are the adjacent sides?

Adjacent sides are next to each other, not across from each other. In the diagram, look for two sides that meet at a corner - those are your adjacent sides with lengths 8 and 3.

What if I'm given different side measurements?

The method stays the same! Just identify the two different side lengths (adjacent sides), then use $P = 2(a + b)$ . Remember: opposite sides are always equal in parallelograms.

Can I just add all four sides individually?

Yes, but it's more work! You'd get 8 + 3 + 8 + 3 = 22. The formula $P = 2(a + b)$ is faster and less prone to addition errors.

What's the difference between a parallelogram and a rectangle?

A rectangle is a special type of parallelogram where all angles are 90°. Both have opposite sides equal, so the perimeter formula $P = 2(a + b)$ works for both shapes!

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