Calculate Parallelogram Perimeter: Finding the Total Length with Sides 4 and 5

Parallelogram Perimeter with Two Adjacent Sides

Given the parallelogram:

555444AAABBBDDDCCC

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
00:13 Let's substitute the side value
00:20 These sides are also opposite therefore equal
00:26 Let's substitute the side value
00:35 The perimeter of the parallelogram equals the sum of its sides
00:53 Let's substitute appropriate values and solve to find the perimeter
01:03 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:

555444AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

2

Step-by-step solution

To solve the problem of calculating the perimeter of the parallelogram, follow these steps:

  • Identify the given side lengths: AB=5 AB = 5 and AC=4 AC = 4 .
  • Acknowledge that in a parallelogram, opposite sides are equal, so AB=CD=5 AB = CD = 5 and AC=BD=4 AC = BD = 4 .
  • Apply the perimeter formula for a parallelogram: P=2×(Base+Side) P = 2 \times ( \text{Base} + \text{Side} ) .

Plug the known side lengths into the formula:
P=2×(AB+AC)=2×(5+4)=2×9=18 P = 2 \times (AB + AC) = 2 \times (5 + 4) = 2 \times 9 = 18

Thus, the perimeter of the parallelogram is 18 18 .

3

Final Answer

18

Key Points to Remember

Essential concepts to master this topic
  • Property: Opposite sides of parallelograms are always equal in length
  • Formula: P = 2(a + b) where a = 5 and b = 4
  • Check: Count all four sides: 5 + 4 + 5 + 4 = 18 ✓

Common Mistakes

Avoid these frequent errors
  • Adding only the two given sides
    Don't just add 5 + 4 = 9! This ignores that parallelograms have four sides, not two. The perimeter needs ALL sides around the shape. Always use the formula P = 2(a + b) to account for both pairs of opposite 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 perimeter formula?

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Because a parallelogram has two pairs of opposite sides! If one side is 5, then its opposite side is also 5. Same for the 4-unit sides. So you have: 5 + 4 + 5 + 4, which equals 2(5 + 4).

How do I know which sides are opposite in a parallelogram?

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Opposite sides are the ones that don't touch each other. In the diagram, sides AB and CD are opposite (both length 5), and sides AC and BD are opposite (both length 4).

What if the parallelogram looks tilted or slanted?

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The shape doesn't matter for perimeter! Whether it's a rectangle, rhombus, or slanted parallelogram, the perimeter formula stays the same: P = 2(a + b).

Can I just count the sides I see in the picture?

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Be careful! Sometimes diagrams only label two adjacent sides because the opposite sides are automatically equal. Always use the given measurements and the parallelogram property.

Is there a difference between perimeter of rectangles and parallelograms?

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No! Rectangles are special parallelograms, so they use the same perimeter formula: P = 2(length + width). The calculation method is identical.

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