Calculate Parallelogram Perimeter: Finding the Total Length with 3-Unit Base

Parallelogram Perimeter with Given Side Measurements

Calculate the perimeter of the following parallelogram:

333111

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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
00:14 The perimeter of the parallelogram equals the sum of its sides
00:33 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

Calculate the perimeter of the following parallelogram:

333111

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the base and side of the parallelogram from the diagram.
  • Step 2: Use the perimeter formula for a parallelogram.
  • Step 3: Substitute the values into the formula to find the perimeter.

Now, let's work through each step:
Step 1: From the diagram, the base of the parallelogram is given as 3 3 units (top side). Despite the lack of explicit vertical length values, the common approach is to assume symmetrical side lengths—both the base and the side given symmetrically leads us to a second side, typically directly inferred. However, since all clear interpretation points to utilizing 1 and horizontal 3, we verify with associated edge matching.
Step 2: Use the formula for the perimeter of the parallelogram: P=2×(base+side) P = 2 \times (\text{base} + \text{side}) .
Step 3: Substitute the given values into the formula: P=2×(3+1) P = 2 \times (3 + 1) .
Calculating this gives us: P=2×4=8 P = 2 \times 4 = 8 .

Therefore, the solution to the problem is P=8 P = 8 .

3

Final Answer

8

Key Points to Remember

Essential concepts to master this topic
  • Formula: Perimeter equals 2 times the sum of base plus side
  • Technique: Use P=2×(3+1)=8 P = 2 \times (3 + 1) = 8 units
  • Check: Verify opposite sides are equal: 3+1+3+1 = 8 units ✓

Common Mistakes

Avoid these frequent errors
  • Adding all four sides without recognizing opposite sides are equal
    Don't measure or add each side individually without using the parallelogram property = wastes time and increases error risk! Students often forget that opposite sides in parallelograms are always equal. Always use the formula P = 2(base + side) to avoid confusion.

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 the base is 3 and the side is 1, you have two sides of length 3 and two sides of length 1.

How do I know which measurement is the base and which is the side?

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It doesn't matter for calculating perimeter! Whether you call the 3-unit length the base or side, you still get P = 2(3 + 1) = 8. The formula works either way.

What if the diagram doesn't clearly show all the measurements?

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Look for parallel markings or labels on the diagram. In parallelograms, you only need two adjacent sides because opposite sides are always equal in length.

Can I just add 3 + 1 + 3 + 1 instead of using the formula?

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Yes, that works too! You get the same answer: 8 units. However, using P = 2(base + side) is faster and helps you remember the parallelogram property.

What's the difference between area and perimeter of a parallelogram?

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  • Perimeter: The distance around the outside (add all sides)
  • Area: The space inside (base × height, which is different from side length)

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