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:

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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

00:06 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

Find the perimeter of the parallelogram using the data below.

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

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