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:

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?

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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