Calculate Parallelogram Perimeter: Given Sides 10 and 8 Units

Parallelogram Perimeter with Given Side Lengths

Given the parallelogram:

101010888AAABBBDDDCCC

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
00:07 Let's substitute the side value
00:15 These sides are also opposite therefore equal
00:19 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 problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the parallelogram:

101010888AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

2

Step-by-step solution

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

  • Step 1: Identify the lengths of the sides of the parallelogram.
  • Step 2: Apply the perimeter formula for a parallelogram.
  • Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: The given information tells us that one side AB AB is 10 10 , and the adjacent side AC AC is 8 8 .
Step 2: The perimeter P P of a parallelogram is given by the formula P=2×(base+side) P = 2 \times (\text{base} + \text{side}) .
Step 3: We substitute the lengths we have: P=2×(10+8)=2×18=36 P = 2 \times (10 + 8) = 2 \times 18 = 36

Therefore, the perimeter of the parallelogram is 36 36 .

3

Final Answer

36

Key Points to Remember

Essential concepts to master this topic
  • Rule: In parallelograms, opposite sides are equal in length
  • Formula: Perimeter = 2 × (side₁ + side₂) = 2 × (10 + 8)
  • Check: Count all four sides: 10 + 8 + 10 + 8 = 36 ✓

Common Mistakes

Avoid these frequent errors
  • Adding only the two given side lengths
    Don't calculate 10 + 8 = 18 as the final answer! This only counts two sides, not all four. A parallelogram has four sides total. Always use the formula P = 2 × (side₁ + side₂) to account for all 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 four sides, but opposite sides are equal! So you have two sides of length 10 and two sides of length 8. Instead of adding 10 + 8 + 10 + 8, it's easier to calculate 2 × (10 + 8).

What if I'm only given one side length?

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You need both adjacent sides to find the perimeter. If you only know one side, you cannot calculate the perimeter unless the parallelogram is actually a special case like a rhombus (all sides equal).

Does it matter which two sides I use in the formula?

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No! You can use any two adjacent sides (sides that meet at a corner). In this problem, you could use 10 and 8, and the formula P=2×(10+8) P = 2 × (10 + 8) gives you 36.

Is this the same formula for rectangles?

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Yes! Rectangles are special parallelograms, so they use the same perimeter formula. The only difference is that rectangles have right angles, but the side relationships are identical.

How can I remember which sides are equal?

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Think of a parallelogram as a "pushed rectangle" - the opposite sides stay parallel and equal. If you label the corners A, B, C, D going around, then AB = CD and AC = BD.

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