Calculate Parallelogram Perimeter: 10-Unit Base with 8-Unit Side

Q: Why do I multiply by 2 in the formula P = 2(a + b)?

Because a parallelogram has four sides, but opposite sides are equal! You have two sides of length 10 and two sides of length 8, so doubling the sum gives you all four sides.

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

You need both adjacent side lengths to find the perimeter. A parallelogram isn't a square, so not all sides are equal - you must know both different side lengths.

Q: Can I just count the sides in the diagram?

The diagram shows the shape, but you need to use the given measurements (10 and 8). Counting visually won't give you accurate numerical lengths.

Q: Is there a difference between base and side in a parallelogram?

No mathematical difference for perimeter! Whether you call them base/side or side/side, you still need both lengths and use the same formula: $ P = 2(a + b) $.

Q: How do I know which sides are equal to each other?

In any parallelogram, opposite sides are equal. So if one side is 10 units, the side across from it is also 10 units. Same with the 8-unit sides.

Parallelogram Perimeter with Given Side Lengths

Calculate the perimeter of the following parallelogram:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's calculate the perimeter of a parallelogram.

00:12 Remember, opposite sides of a parallelogram are equal.

00:19 To find the perimeter, add up the lengths of all the sides.

00:34 And that's how you solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the perimeter of the following parallelogram:

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate perimeter formula for the parallelogram
Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us the lengths of two adjacent sides of the parallelogram: $a = 10$ and $b = 8$ .
Step 2: We'll use the formula for the perimeter of a parallelogram: $P = 2(a + b)$ .
Step 3: Plugging in our values, we get:

$P = 2(10 + 8) = 2 \times 18 = 36$

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter of parallelogram equals 2(a + b)
Technique: Add adjacent sides first: 10 + 8 = 18, then multiply by 2
Check: Count all four sides: 10 + 8 + 10 + 8 = 36 ✓

Common Mistakes

Avoid these frequent errors

Adding all sides without using the parallelogram property
Don't just add 10 + 8 = 18 and stop there! This only gives half the perimeter. Opposite sides in parallelograms are equal, so you have four sides total. Always use P = 2(a + b) or count all four sides: 10 + 8 + 10 + 8.

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 do I multiply by 2 in the formula P = 2(a + b)?

Because a parallelogram has four sides, but opposite sides are equal! You have two sides of length 10 and two sides of length 8, so doubling the sum gives you all four sides.

What if I'm only given one side length?

You need both adjacent side lengths to find the perimeter. A parallelogram isn't a square, so not all sides are equal - you must know both different side lengths.

Can I just count the sides in the diagram?

The diagram shows the shape, but you need to use the given measurements (10 and 8). Counting visually won't give you accurate numerical lengths.

Is there a difference between base and side in a parallelogram?

No mathematical difference for perimeter! Whether you call them base/side or side/side, you still need both lengths and use the same formula: $P = 2(a + b)$ .

How do I know which sides are equal to each other?

In any parallelogram, opposite sides are equal. So if one side is 10 units, the side across from it is also 10 units. Same with the 8-unit sides.

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