Calculate Parallelogram Perimeter: Given Sides 20 and 15 Units

Parallelogram Perimeter with Given Adjacent Sides

Given the parallelogram:

202020151515AAABBBDDDCCC

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
00:13 These sides are also opposite therefore equal
00:18 Let's substitute the side value
00:29 The perimeter of the parallelogram equals the sum of its sides
00:47 Let's substitute appropriate values and solve for the perimeter
00:53 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:

202020151515AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

2

Step-by-step solution

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

  • Step 1: Identify the given side lengths of the parallelogram.
  • Step 2: Use the perimeter formula for a parallelogram, P=2(a+b) P = 2(a + b) .
  • Step 3: Perform the calculation to find the perimeter.

Let's proceed with the solution:

Step 1: The problem provides the side lengths of the parallelogram as AB=20 AB = 20 units and AD=15 AD = 15 units.

Step 2: Use the formula for the perimeter of a parallelogram, P=2(a+b) P = 2(a + b) , where a=20 a = 20 and b=15 b = 15 .

Step 3: Plug the side lengths into the formula:

P=2(20+15)=2×35 P = 2(20 + 15) = 2 \times 35

Calculating further, we get:

P=70 P = 70

Therefore, the perimeter of the parallelogram is 70 70 .

3

Final Answer

70

Key Points to Remember

Essential concepts to master this topic
  • Property: Opposite sides of parallelograms are equal in length
  • Formula: P=2(a+b) P = 2(a + b) where a = 20 and b = 15
  • Check: Two pairs of sides: 20 + 20 + 15 + 15 = 70 ✓

Common Mistakes

Avoid these frequent errors
  • Adding only the two given sides
    Don't just add 20 + 15 = 35 and call it the perimeter! This only gives you half the perimeter since you're missing the other two equal sides. Always remember a parallelogram has 4 sides, so use P = 2(a + b).

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 4 sides arranged in 2 pairs. Each pair has equal lengths, so you have two sides of length 20 and two sides of length 15. The formula P=2(a+b) P = 2(a + b) accounts for both pairs!

What if I only know one side length?

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You need at least two adjacent sides to find the perimeter of a parallelogram. Unlike a square or rectangle, parallelograms can have different side lengths, so one measurement isn't enough.

Are parallelograms the same as rectangles?

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All rectangles are parallelograms, but not all parallelograms are rectangles! Rectangles have the special property that adjacent sides can be equal, but general parallelograms have two different side lengths.

Can I just count the sides in the diagram?

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While you can see there are 4 sides, you still need to use the given measurements. The diagram shows sides labeled 20 and 15, and you need to apply the parallelogram property that opposite sides are equal.

What's the difference between perimeter and area?

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Perimeter is the distance around the outside (what we're calculating here), while area is the space inside the shape. For perimeter, you add up all the side lengths!

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