Calculate Parallelogram Perimeter: Given Sides 14 and 11 Units

Q: Why can't I just add 14 + 11 to get the perimeter?

Because that only gives you two sides of the parallelogram! A perimeter means going all the way around the shape. Since opposite sides are equal, you need 14 + 11 + 14 + 11 = 50.

Q: How do I know which sides are opposite in a parallelogram?

In parallelogram ABCD, the opposite sides are AB & CD (both 14 units) and BC & AD (both 11 units). Opposite sides never touch each other directly.

Q: Is the perimeter formula the same for all parallelograms?

Yes! The formula $ P = 2(a + b) $ works for any parallelogram, including rectangles and squares, because opposite sides are always equal.

Q: What if I'm given the perimeter and need to find a side length?

Use the same formula but solve for the unknown! If $ P = 50 $ and one side is 14, then $ 50 = 2(14 + b) $, so b = 11.

Q: Do I need to know the angles to find the perimeter?

No! Perimeter only depends on side lengths, not angles. Whether the parallelogram is tall, short, or slanted doesn't matter for calculating perimeter.

Perimeter Formulas with Opposite Side Properties

Given the parallelogram:

Calculate the perimeter of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's find out how to calculate the perimeter of a parallelogram.

00:07 Remember, opposite sides in a parallelogram are equal.

00:12 Okay, let's replace one side with the given value and move on.

00:18 These sides are opposite, so they're equal too.

00:23 Now, substitute the other side's value in just like before.

00:35 To find the perimeter, add up all the side lengths of the parallelogram.

00:51 Let's plug in the numbers and calculate the perimeter.

01:00 And there we go! That's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the parallelogram:

Calculate the perimeter of the parallelogram.

Step-by-step solution

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

Step 1: Identify the side lengths of the parallelogram.
Step 2: Apply the perimeter formula for a parallelogram.
Step 3: Calculate the perimeter using the given side lengths.

Now, let's work through each step:
Step 1: The side lengths given are $a = 14$ and $b = 11$ .
Step 2: Apply the formula for the perimeter of a parallelogram, which is $P = 2(a + b)$ .
Step 3: Substitute the values into the formula: $P = 2(14 + 11) = 2 \times 25 = 50$ .

Therefore, the solution to the problem is $P = 50$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are always equal in length
Formula: P = 2(a + b) where a = 14 and b = 11
Check: Count all four sides: 14 + 11 + 14 + 11 = 50 ✓

Common Mistakes

Avoid these frequent errors

Adding only the two given side lengths
Don't calculate 14 + 11 = 25 as the final answer! This only gives you half the perimeter because you forgot the opposite sides. Always use P = 2(a + b) to account for all four sides of the parallelogram.

Practice Quiz

Test your knowledge with interactive questions

Given the parallelogram of the figure

What is your area?

FAQ

Everything you need to know about this question

Why can't I just add 14 + 11 to get the perimeter?

Because that only gives you two sides of the parallelogram! A perimeter means going all the way around the shape. Since opposite sides are equal, you need 14 + 11 + 14 + 11 = 50.

How do I know which sides are opposite in a parallelogram?

In parallelogram ABCD, the opposite sides are AB & CD (both 14 units) and BC & AD (both 11 units). Opposite sides never touch each other directly.

Is the perimeter formula the same for all parallelograms?

Yes! The formula $P = 2(a + b)$ works for any parallelogram, including rectangles and squares, because opposite sides are always equal.

What if I'm given the perimeter and need to find a side length?

Use the same formula but solve for the unknown! If $P = 50$ and one side is 14, then $50 = 2(14 + b)$ , so b = 11.

Do I need to know the angles to find the perimeter?

No! Perimeter only depends on side lengths, not angles. Whether the parallelogram is tall, short, or slanted doesn't matter for calculating perimeter.

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