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 of the figure

What is your area?

7cm7cm7cmAAABBBCCCDDDEEE4cm

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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