Calculate Parallelogram Perimeter: Using Side Lengths 8 and 3

Parallelogram Perimeter with Adjacent Side Measurements

Given the parallelogram:

888333AAABBBDDDCCC

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
00:09 Let's substitute the side value
00:19 These sides are also opposite therefore equal
00:24 Let's substitute the side value
00:34 The perimeter of the parallelogram equals the sum of its sides
00:54 Let's substitute appropriate values and solve for the perimeter
01:07 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:

888333AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

2

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) 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 a = 8 units and b=3 b = 3 units.

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

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

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

Therefore, the perimeter of the parallelogram is 22 22 .

3

Final Answer

22

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:

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 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) P = 2(a + b) .

How do I know which measurements are the adjacent sides?

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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?

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

Can I just add all four sides individually?

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

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

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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) P = 2(a + b) works for both shapes!

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