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

Parallelogram Perimeter with Adjacent Sides

Given the parallelogram:

6.56.56.5AAABBBDDDCCC4.5

Calculate the perimeter of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the perimeter of the parallelogram
00:03 Opposite sides are equal in a parallelogram
00:08 Let's substitute the side value
00:16 These sides are also opposite therefore equal
00:19 Let's substitute the side value
00:32 The perimeter of the parallelogram equals the sum of its sides
00:47 Let's substitute appropriate values and solve for the perimeter
00:57 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the parallelogram:

6.56.56.5AAABBBDDDCCC4.5

Calculate the perimeter of the parallelogram.

2

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

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

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

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

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

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

3

Final Answer

22

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:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

FAQ

Everything you need to know about this question

Why do I multiply by 2 in the formula?

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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) P = 2(a + b) !

What if I just add all four sides individually?

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

How do I know which sides are adjacent?

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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?

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

Can I use this formula for any parallelogram?

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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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