Calculate Parallelogram Perimeter: Given Sides 10 and 8 Units

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

Because a parallelogram has four sides, but opposite sides are equal! So you have two sides of length 10 and two sides of length 8. Instead of adding 10 + 8 + 10 + 8, it's easier to calculate 2 × (10 + 8).

Q: What if I'm only given one side length?

You need both adjacent sides to find the perimeter. If you only know one side, you cannot calculate the perimeter unless the parallelogram is actually a special case like a rhombus (all sides equal).

Q: Does it matter which two sides I use in the formula?

No! You can use any two adjacent sides (sides that meet at a corner). In this problem, you could use 10 and 8, and the formula $ P = 2 × (10 + 8) $ gives you 36.

Q: Is this the same formula for rectangles?

Yes! Rectangles are special parallelograms, so they use the same perimeter formula. The only difference is that rectangles have right angles, but the side relationships are identical.

Q: How can I remember which sides are equal?

Think of a parallelogram as a "pushed rectangle" - the opposite sides stay parallel and equal. If you label the corners A, B, C, D going around, then AB = CD and AC = BD.

Parallelogram Perimeter with Given 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

00:07 Let's substitute the side value

00:15 These sides are also opposite therefore equal

00:19 Let's substitute the side value

00:29 The perimeter of the parallelogram equals the sum of its sides

00:45 Let's substitute appropriate values and solve for the perimeter

00:55 And this is the solution to the 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 solve this problem, we'll follow these steps:

Step 1: Identify the lengths of the sides of the parallelogram.
Step 2: Apply the perimeter formula for a parallelogram.
Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: The given information tells us that one side $AB$ is $10$ , and the adjacent side $AC$ is $8$ .
Step 2: The perimeter $P$ of a parallelogram is given by the formula $P = 2 \times (\text{base} + \text{side})$ .
Step 3: We substitute the lengths we have: $P = 2 \times (10 + 8) = 2 \times 18 = 36$

Therefore, the perimeter of the parallelogram is $36$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: In parallelograms, opposite sides are equal in length
Formula: Perimeter = 2 × (side₁ + side₂) = 2 × (10 + 8)
Check: Count all four sides: 10 + 8 + 10 + 8 = 36 ✓

Common Mistakes

Avoid these frequent errors

Adding only the two given side lengths
Don't calculate 10 + 8 = 18 as the final answer! This only counts two sides, not all four. A parallelogram has four sides total. Always use the formula P = 2 × (side₁ + side₂) to account for all sides.

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 do I multiply by 2 in the perimeter formula?

Because a parallelogram has four sides, but opposite sides are equal! So you have two sides of length 10 and two sides of length 8. Instead of adding 10 + 8 + 10 + 8, it's easier to calculate 2 × (10 + 8).

What if I'm only given one side length?

You need both adjacent sides to find the perimeter. If you only know one side, you cannot calculate the perimeter unless the parallelogram is actually a special case like a rhombus (all sides equal).

Does it matter which two sides I use in the formula?

No! You can use any two adjacent sides (sides that meet at a corner). In this problem, you could use 10 and 8, and the formula $P = 2 × (10 + 8)$ gives you 36.

Is this the same formula for rectangles?

Yes! Rectangles are special parallelograms, so they use the same perimeter formula. The only difference is that rectangles have right angles, but the side relationships are identical.

How can I remember which sides are equal?

Think of a parallelogram as a "pushed rectangle" - the opposite sides stay parallel and equal. If you label the corners A, B, C, D going around, then AB = CD and AC = BD.

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