Parallelogram Perimeter: Calculate with Side Lengths 5 and 2

Q: Why do I multiply by 2 in the perimeter formula?

A parallelogram has four sides, but opposite sides are equal! So if you know two adjacent sides (5 and 2), you actually know all four sides: 5, 2, 5, 2. The formula $ P = 2(a + b) $ is a shortcut for adding all four.

Q: What if I only know one side length?

You need both different side lengths to find a parallelogram's perimeter! Unlike a square where all sides are equal, parallelograms have two pairs of equal sides with different lengths.

Q: How is this different from a rectangle's perimeter?

It's exactly the same! A rectangle is actually a special type of parallelogram, so they use the same perimeter formula: $ P = 2(\text{length} + \text{width}) $.

Q: What if the numbers were different, like 8 and 3?

Just substitute into the formula! $ P = 2(8 + 3) = 2(11) = 22 $. The method stays the same regardless of the actual measurements.

Parallelogram Perimeter with Given Side Lengths

Find the perimeter of the parallelogram using the data below.

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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

00:11 The perimeter of the parallelogram equals the sum of its sides

00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the perimeter of the parallelogram using the data below.

Step-by-step solution

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

Step 1: Identify the given lengths of the parallelogram.
Step 2: Apply the perimeter formula for a parallelogram.
Step 3: Perform the calculation to find the perimeter.

Now, let's work through each step:
Step 1: We are given that the length of the base is $5$ units and the slant height or the side length is $2$ units.
Step 2: The formula for the perimeter of a parallelogram is:

$P = 2 \times (\text{Base} + \text{Side})$

Step 3: Plugging in the given values:

$P = 2 \times (5 + 2) = 2 \times 7 = 14$

Therefore, the perimeter of the parallelogram is $14$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals 2 times the sum of adjacent sides
Calculation: $P = 2 \times (5 + 2) = 14$ units
Check: Count all four sides: 5 + 2 + 5 + 2 = 14 ✓

Common Mistakes

Avoid these frequent errors

Adding all given measurements once instead of doubling
Don't just add 5 + 2 = 7! This only gives you half the perimeter because a parallelogram has four sides, not two. Always remember that opposite sides are equal, so multiply by 2.

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 do I multiply by 2 in the perimeter formula?

A parallelogram has four sides, but opposite sides are equal! So if you know two adjacent sides (5 and 2), you actually know all four sides: 5, 2, 5, 2. The formula $P = 2(a + b)$ is a shortcut for adding all four.

What if I only know one side length?

You need both different side lengths to find a parallelogram's perimeter! Unlike a square where all sides are equal, parallelograms have two pairs of equal sides with different lengths.

How is this different from a rectangle's perimeter?

It's exactly the same! A rectangle is actually a special type of parallelogram, so they use the same perimeter formula: $P = 2(\text{length} + \text{width})$ .

Can I just count the sides in the diagram?

Yes, but be careful! The diagram shows a parallelogram with sides labeled 5 and 2. Count all four sides: 5 + 2 + 5 + 2 = 14. The formula is just a faster way to do the same thing.

What if the numbers were different, like 8 and 3?

Just substitute into the formula! $P = 2(8 + 3) = 2(11) = 22$ . The method stays the same regardless of the actual measurements.

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