Calculate Parallelogram Perimeter: Finding Total Length with 6.5 and 4.5 Unit Sides

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

A parallelogram has four sides, but opposite sides are equal. So you have two sides of length 6.5 and two sides of length 4.5. That's why we use $ P = 2(a + b) $!

Q: How do I know which sides are adjacent?

Adjacent sides are sides that share a vertex (corner). In the diagram, sides AB and AD are adjacent because they both connect to point A. Opposite sides are parallel and equal.

Q: What if the parallelogram looks like a rectangle?

The formula still works! A rectangle is a special type of parallelogram where all angles are 90°. You still use $ P = 2(length + width) $.

Q: Can I use this formula for any parallelogram?

Yes! This perimeter formula works for all parallelograms - rectangles, squares, rhombuses, and general parallelograms. Just identify the two different side lengths.

Parallelogram Perimeter with Adjacent Sides

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

00:05 We're going to calculate the perimeter of a parallelogram.

00:09 Remember, opposite sides in a parallelogram are equal.

00:14 Now, let's substitute the value of one side.

00:21 These sides are also opposite, so they are equal too.

00:25 Let's fill in the value for this side as well.

00:37 The perimeter is the sum of all sides.

00:52 Substitute the values and solve for the perimeter.

01:02 And that's how we find the perimeter of this parallelogram.

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 determine the perimeter of the parallelogram, follow these steps:

Step 1: Note the given side lengths of the parallelogram. Side $AB = 6.5$ and side $AD = 4.5$ .
Step 2: Apply the perimeter formula for a parallelogram: $P = 2(a + b)$ , where $a$ and $b$ are the lengths of two adjacent sides.
Step 3: Substitute the given lengths into the formula:

$P = 2 \times (6.5 + 4.5)$

Step 4: Perform the addition inside the parentheses: $6.5 + 4.5 = 11$

Step 5: Multiply the sum by 2 to find the perimeter: $P = 2 \times 11 = 22$

Therefore, the solution to the problem is that the perimeter of the parallelogram is $P = 22$ .

Upon reviewing the choices, the correct answer is choice 4: 22.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals 2 times sum of adjacent sides
Calculation: P = 2(6.5 + 4.5) = 2(11) = 22
Check: Add all four sides: 6.5 + 4.5 + 6.5 + 4.5 = 22 ✓

Common Mistakes

Avoid these frequent errors

Adding only two sides instead of using the perimeter formula
Don't just add 6.5 + 4.5 = 11! This only gives you half the perimeter because parallelograms have four sides, not two. Always use P = 2(a + b) to account for all four 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 formula?

A parallelogram has four sides, but opposite sides are equal. So you have two sides of length 6.5 and two sides of length 4.5. That's why we use $P = 2(a + b)$ !

What if I just add all four sides individually?

That works perfectly too! You'd get 6.5 + 4.5 + 6.5 + 4.5 = 22. The formula $P = 2(a + b)$ is just a faster way to do the same calculation.

How do I know which sides are adjacent?

Adjacent sides are sides that share a vertex (corner). In the diagram, sides AB and AD are adjacent because they both connect to point A. Opposite sides are parallel and equal.

What if the parallelogram looks like a rectangle?

The formula still works! A rectangle is a special type of parallelogram where all angles are 90°. You still use $P = 2(length + width)$ .

Can I use this formula for any parallelogram?

Yes! This perimeter formula works for all parallelograms - rectangles, squares, rhombuses, and general parallelograms. Just identify the two different side lengths.

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