Calculate Parallelogram Perimeter: Finding Total Length with Sides 5 and 2

Q: Why can't I just add 5 + 2 to get the perimeter?

Because perimeter means the total distance around the entire shape! A parallelogram has four sides, not just two. You need to add all four: 5 + 2 + 5 + 2 = 14.

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

Opposite sides are always equal in a parallelogram. If one side is 5 and an adjacent side is 2, then the opposite sides are also 5 and 2 respectively.

Q: Is there a faster way than adding all four sides?

Yes! Use the formula $ P = 2(a + b) $ where a and b are adjacent sides. This automatically doubles the sum: $ P = 2(5 + 2) = 2 \times 7 = 14 $.

Q: What if I'm given different side lengths?

The method stays the same! Just identify the two different adjacent sides, add them together, then multiply by 2. The formula $ P = 2(a + b) $ works for any parallelogram.

Q: How is this different from finding the area?

Perimeter is the distance around the outside (measured in units like cm), while area is the space inside (measured in square units like cm²). For perimeter, you only need the side lengths!

Parallelogram Perimeter with Given Adjacent Sides

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

00:00 Calculate the perimeter of the parallelogram

00:03 Opposite sides are equal in a parallelogram

00:07 Let's substitute the side value

00:14 These sides are also opposite therefore equal

00:20 Let's substitute the side value

00:28 The perimeter of the parallelogram equals the sum of its sides

00:50 Let's substitute appropriate values and solve for the perimeter

00:58 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

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 given side lengths of the parallelogram.
Step 2: Apply the perimeter formula for a parallelogram.
Step 3: Perform the calculation with the identified side lengths.

Now, let's work through each step:
Step 1: The problem gives us the side lengths of the parallelogram as $AB = 5$ and $BC = 2$ . Since opposite sides are equal in a parallelogram, we have $AB = CD = 5$ and $BC = DA = 2$ .
Step 2: We'll use the formula for the perimeter of a parallelogram: $P = 2(a + b)$ .
Step 3: Substituting the values, we have:

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

Therefore, the perimeter of the parallelogram is $\boxed{14}$ .

The correct multiple-choice answer is 14, which corresponds to choice number 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are always equal in length
Formula: Perimeter = 2(a + b) where a = 5 and b = 2
Check: Count all four sides: 5 + 2 + 5 + 2 = 14 ✓

Common Mistakes

Avoid these frequent errors

Adding only two adjacent sides instead of all four
Don't just calculate 5 + 2 = 7 as the perimeter! This only gives you half the distance around. A parallelogram has four sides, so you must count each side: two sides of length 5 and two sides of length 2. Always use the formula P = 2(a + b) to account for all four sides.

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 5 + 2 to get the perimeter?

Because perimeter means the total distance around the entire shape! A parallelogram has four sides, not just two. You need to add all four: 5 + 2 + 5 + 2 = 14.

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

Opposite sides are always equal in a parallelogram. If one side is 5 and an adjacent side is 2, then the opposite sides are also 5 and 2 respectively.

Is there a faster way than adding all four sides?

Yes! Use the formula $P = 2(a + b)$ where a and b are adjacent sides. This automatically doubles the sum: $P = 2(5 + 2) = 2 \times 7 = 14$ .

What if I'm given different side lengths?

The method stays the same! Just identify the two different adjacent sides, add them together, then multiply by 2. The formula $P = 2(a + b)$ works for any parallelogram.

How is this different from finding the area?

Perimeter is the distance around the outside (measured in units like cm), while area is the space inside (measured in square units like cm²). For perimeter, you only need the side lengths!

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