Calculate Parallelogram Perimeter: Finding the Total Length with Side Measurements 2 and 4

Parallelogram Perimeter with Given Side Lengths

Given the parallelogram:

444222AAABBBDDDCCC

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
00:12 These sides are also opposite therefore equal
00:17 Let's substitute the side value
00:29 The perimeter of the parallelogram equals the sum of its sides
00:45 Let's substitute appropriate values and solve for the perimeter
00:55 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

2

Step-by-step solution

To find the perimeter of the parallelogram, we follow these steps:

  • Step 1: Identify the given side lengths from the diagram: AB=4 AB = 4 units and AD=2 AD = 2 units.
  • Step 2: Use the perimeter formula for a parallelogram, which is P=2(a+b) P = 2(a + b) .
  • Step 3: Substituting the given values into the formula: a=4 a = 4 and b=2 b = 2 .

Proceeding with the calculation:

P=2(4+2)=2×6=12 P = 2(4 + 2) = 2 \times 6 = 12 .

Therefore, the perimeter of the parallelogram is 12 units.

3

Final Answer

12

Key Points to Remember

Essential concepts to master this topic
  • Formula: Parallelogram perimeter equals 2(a + b) where a and b are adjacent sides
  • Technique: Identify opposite sides are equal: AB = CD = 4 and AD = BC = 2
  • Check: Count all four sides: 4 + 2 + 4 + 2 = 12 units ✓

Common Mistakes

Avoid these frequent errors
  • Adding only the two given sides
    Don't calculate 4 + 2 = 6 as the final answer! This only counts two sides when a parallelogram has four sides. Always remember that opposite sides are equal, so multiply by 2: 2(4 + 2) = 12.

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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A parallelogram has four sides, but opposite sides are equal in length. So instead of adding all four sides separately, we add the two different side lengths and multiply by 2!

How do I know which sides are equal?

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In a parallelogram, opposite sides are always equal. If you see sides labeled 4 and 2, then the opposite sides are also 4 and 2 respectively.

Can I just add all four sides individually?

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Yes! You can add 4 + 2 + 4 + 2 = 12. The formula P=2(a+b) P = 2(a + b) is just a shortcut that gives the same result more quickly.

What if the parallelogram looks tilted or slanted?

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The shape doesn't matter for perimeter! Whether the parallelogram is a rectangle, rhombus, or slanted, you still add up all four side lengths the same way.

Do I need to worry about the angles?

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No! Perimeter only depends on the lengths of the sides, not the angles. The angles don't affect how far you'd walk around the edge.

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