Calculate Parallelogram Perimeter: Using Side Lengths 4 and 6

Q: Why are opposite sides equal in a parallelogram?

By definition, a parallelogram has two pairs of parallel sides. When sides are parallel and connected, the opposite sides must be equal in length. This is a fundamental property!

Q: Do I need to measure all four sides?

No! Since opposite sides are equal, you only need to know two adjacent sides. Then double each measurement: if one side is 4 and the adjacent side is 6, the perimeter is $ 2(4) + 2(6) = 20 $.

Q: Is there a formula for parallelogram perimeter?

Yes! The formula is $ P = 2a + 2b $ where a and b are the lengths of two adjacent sides. This is the same as $ P = 2(a + b) $.

Q: What if the parallelogram looks tilted or slanted?

The shape doesn't matter for perimeter! Whether the parallelogram is a rectangle, rhombus, or slanted, you still add up all four side lengths the same way.

Q: How can I double-check my perimeter calculation?

Count that you used exactly four sidesVerify opposite sides are equal: AB = CD and AC = BDUse the formula $ P = 2(a + b) $ as a second method

Parallelogram Perimeter with Equal Opposite Sides

Calculate the perimeter of the given parallelogram:

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of the parallelogram

00:06 Opposite sides are equal in a parallelogram

00:16 Let's substitute the side value

00:25 These sides are also opposite therefore equal

00:32 Let's substitute the side value

00:38 The perimeter of the parallelogram equals the sum of its sides

01:02 Let's substitute appropriate values and solve for the perimeter

01:13 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

Calculate the perimeter of the given parallelogram:

Step-by-step solution

As is true for a parallelogram every pair of opposite sides are equal:

$AB=CD=6,AC=BD=4$

The perimeter of the parallelogram is equal to the sum of all sides together:

$4+4+6+6=8+12=20$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: In parallelograms, opposite sides are always equal in length
Method: Add all four sides: 4 + 4 + 6 + 6 = 20
Check: Count each side once: two sides of 4 and two sides of 6 ✓

Common Mistakes

Avoid these frequent errors

Adding only two different side lengths instead of all four sides
Don't just add 4 + 6 = 10! This only counts two sides, not the complete perimeter. A parallelogram has four sides total. Always add all four sides: 4 + 4 + 6 + 6 = 20.

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 are opposite sides equal in a parallelogram?

By definition, a parallelogram has two pairs of parallel sides. When sides are parallel and connected, the opposite sides must be equal in length. This is a fundamental property!

Do I need to measure all four sides?

No! Since opposite sides are equal, you only need to know two adjacent sides. Then double each measurement: if one side is 4 and the adjacent side is 6, the perimeter is $2(4) + 2(6) = 20$ .

Is there a formula for parallelogram perimeter?

Yes! The formula is $P = 2a + 2b$ where a and b are the lengths of two adjacent sides. This is the same as $P = 2(a + b)$ .

What if the parallelogram looks tilted or slanted?

The shape doesn't matter for perimeter! Whether the parallelogram is a rectangle, rhombus, or slanted, you still add up all four side lengths the same way.

How can I double-check my perimeter calculation?

Count that you used exactly four sides
Verify opposite sides are equal: AB = CD and AC = BD
Use the formula $P = 2(a + b)$ as a second method

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime