Calculate Parallelogram Perimeter: Given Side Lengths 3 and 9

Q: Why can't I just add 9 + 3 to get the perimeter?

Because a parallelogram has four sides, not two! You're given the lengths of two adjacent sides, but you need to account for all four sides. Since opposite sides are equal, you have sides of 9, 3, 9, and 3.

Q: How do I know which sides are equal?

In any parallelogram, opposite sides are always equal. If one side is 9 units, the side directly across from it is also 9 units. Same for the 3-unit sides!

Q: What's the difference between adjacent and opposite sides?

Adjacent sides: Next to each other, sharing a vertexOpposite sides: Across from each other, parallel and equalThe problem gives you two adjacent sides: 9 and 3.

Q: Can I use this formula for any parallelogram?

Yes! The formula $ P = 2(a + b) $ works for any parallelogram, including rectangles and squares. Just identify two adjacent sides and apply the formula.

Q: What if the parallelogram looks tilted or slanted?

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

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

00:03 Let's find the perimeter of this parallelogram.

00:07 Remember, in a parallelogram, opposite sides are equal.

00:12 Now, let's insert the length of one side.

00:17 These other sides are opposite, so they are equal too.

00:23 Let's put in the length of this side as well.

00:35 The perimeter is the total of all the side lengths. Let's add them up!

00:50 We'll plug in the values and calculate the perimeter together.

01:01 And there we have it! That's how we solve this problem.

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 determine the perimeter of the parallelogram, we need first to identify the lengths of the sides:

From the problem, one side ( $a$ ) is $9$ units, and an adjacent side ( $b$ ) is $3$ units.

Using the formula for the perimeter of a parallelogram, $P = 2(a + b)$ , we can substitute the known values:

$a = 9$
$b = 3$

Substituting these values into the formula gives us:

$P = 2(9 + 3)$

$P = 2 \times 12$

$P = 24$

Therefore, the perimeter of the parallelogram is $24$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of a parallelogram are equal in length
Formula: Perimeter = 2(a + b) where a = 9 and b = 3
Check: Count all four sides: 9 + 3 + 9 + 3 = 24 ✓

Common Mistakes

Avoid these frequent errors

Adding only the two given side lengths
Don't calculate 9 + 3 = 12 as the final answer! This only accounts for two sides when a parallelogram has four sides. Always remember that opposite sides are equal, so multiply by 2: Perimeter = 2(9 + 3) = 24.

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 can't I just add 9 + 3 to get the perimeter?

Because a parallelogram has four sides, not two! You're given the lengths of two adjacent sides, but you need to account for all four sides. Since opposite sides are equal, you have sides of 9, 3, 9, and 3.

How do I know which sides are equal?

In any parallelogram, opposite sides are always equal. If one side is 9 units, the side directly across from it is also 9 units. Same for the 3-unit sides!

What's the difference between adjacent and opposite sides?

Adjacent sides: Next to each other, sharing a vertex
Opposite sides: Across from each other, parallel and equal

The problem gives you two adjacent sides: 9 and 3.

Can I use this formula for any parallelogram?

Yes! The formula $P = 2(a + b)$ works for any parallelogram, including rectangles and squares. Just identify two adjacent sides and apply the formula.

What if the parallelogram looks tilted or slanted?

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

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Calculate Parallelogram Perimeter: Given Side Lengths 3 and 9

Parallelogram Perimeter with Adjacent Side Lengths

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just add 9 + 3 to get the perimeter?

How do I know which sides are equal?

What's the difference between adjacent and opposite sides?

Can I use this formula for any parallelogram?

What if the parallelogram looks tilted or slanted?

🌟 Unlock Your Math Potential

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