Calculate Parallelogram Perimeter: Finding the Total Length of a 6 by 8 Shape

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

A parallelogram has 4 sides, but opposite sides are equal! So if you know two adjacent sides (like 8 and 6), you actually know all four sides: 8, 6, 8, 6. Multiplying by 2 counts both pairs.

Q: How do I identify which sides to use in my calculation?

Use any two adjacent sides (sides that meet at a corner). In this parallelogram, we can see sides of length 8 and 6 meeting at vertex A, so these are our a and b values.

Q: What if I only know one side length?

You need at least two different side lengths to find a parallelogram's perimeter. If you only know one side, you can't determine the perimeter unless it's actually a special parallelogram like a rhombus (all sides equal).

Q: Is this the same formula for rectangles?

Yes! A rectangle is a special type of parallelogram, so $ P = 2(length + width) $ is the same as $ P = 2(a + b) $.

Q: Can I just add up all four sides instead?

Absolutely! You can add $ 8 + 6 + 8 + 6 = 28 $. The formula $ P = 2(a + b) $ is just a shortcut that does the same calculation faster.

Parallelogram Perimeter with Adjacent Side Lengths

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

00:08 Let's substitute the side value

00:12 These sides are also opposite therefore equal

00:16 Let's substitute the side value

00:26 The perimeter of the parallelogram equals the sum of its sides

00:47 Let's substitute appropriate values and solve for the perimeter

00:57 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Given the parallelogram:

Calculate the perimeter of the parallelogram.

Step-by-step solution

To calculate the perimeter of the parallelogram ABCD, we need the lengths of its two adjacent sides. Given that one side, AB, is 8 units, and recalling that adjacent parallelogram sides will mirror their opposites, AC represents a relevant measurement within the context—but sides not involved with inclination describe standard periphery bounds without adjustments (hence reliance on visually positioned evaluation without contradictions).

Following the perimeter formula for parallelograms:

P = 2(a + b)

In our shape, let’s define:

$a = 8$ (Length of side AB or its opposite estimation feature equated)
$b = 6$ (Instinctive reconfirmation according to positive iteration; i.e., default parameter for spatial definition)

Plugging these values into our formula, we get:

P = 2(8 + 6)

P = 2(14)

P = 28

Therefore, the perimeter of the parallelogram is $28$ units.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Parallelogram perimeter equals $P = 2(a + b)$
Technique: Add adjacent sides: 8 + 6 = 14, then multiply by 2
Check: Count all four sides: 8 + 6 + 8 + 6 = 28 ✓

Common Mistakes

Avoid these frequent errors

Adding only the given measurements without doubling
Don't just add 8 + 6 = 14! This only counts two sides, not the full perimeter. A parallelogram has 4 sides total - opposite sides are equal. Always use P = 2(a + b) to count 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 do I multiply by 2 in the perimeter formula?

A parallelogram has 4 sides, but opposite sides are equal! So if you know two adjacent sides (like 8 and 6), you actually know all four sides: 8, 6, 8, 6. Multiplying by 2 counts both pairs.

How do I identify which sides to use in my calculation?

Use any two adjacent sides (sides that meet at a corner). In this parallelogram, we can see sides of length 8 and 6 meeting at vertex A, so these are our a and b values.

What if I only know one side length?

You need at least two different side lengths to find a parallelogram's perimeter. If you only know one side, you can't determine the perimeter unless it's actually a special parallelogram like a rhombus (all sides equal).

Is this the same formula for rectangles?

Yes! A rectangle is a special type of parallelogram, so $P = 2(length + width)$ is the same as $P = 2(a + b)$ .

Can I just add up all four sides instead?

Absolutely! You can add $8 + 6 + 8 + 6 = 28$ . The formula $P = 2(a + b)$ is just a shortcut that does the same calculation faster.

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