Calculate the Perimeter: Rectangle Composed of Two Equal Squares

Q: Why isn't the middle line part of the perimeter?

The perimeter is only the outer boundary of a shape. The line BE just shows how the rectangle is made of two squares - it's inside the rectangle, not around it!

Q: How do I know the rectangle's length and width?

Since each square has side length 6, the rectangle's length is two squares side-by-side: 6 + 6 = 12. The width is just one square's side: 6.

Q: Can I use the square perimeter formula instead?

No! This is a rectangle, not a square. Use the rectangle formula: $ P = 2l + 2w $ where length = 12 and width = 6.

Rectangle Perimeter with Square Components

Below is a rectangle composed of two squares.

What is its perimeter?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the perimeter of the rectangle.

00:07 Remember, in a square, all sides are equal.

00:12 Here, the rectangle is made up of two squares.

00:17 So, let's use the side length given.

00:20 According to the data, the sides are equal.

00:29 The perimeter equals the sum of all its sides.

00:33 Let's plug in the values and calculate the perimeter.

00:37 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is a rectangle composed of two squares.

What is its perimeter?

Step-by-step solution

In a square, all sides are equal. Therefore:
$AB+BC+CD+DE+EF+FA=6$

Thus, we find out what the side AC is equal to:

$AC=AB+BC$

$AB=6+6=12$

In a rectangle, we know that the opposite sides are equal to each other, therefore:

$AB=FD=12$

Therefore, the formula for the perimeter of the rectangle will look like this:

$2\times AB+2\times CD$

We replace the data:

$2\times12+2\times6=$

$24+12=36$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Square Properties: All sides equal, so each square side is 6
Rectangle Formation: Length = 6 + 6 = 12, width = 6
Perimeter Check: 2(12) + 2(6) = 24 + 12 = 36 ✓

Common Mistakes

Avoid these frequent errors

Adding all visible segments without understanding rectangle structure
Don't add AB + BC + CD + DE + EF + FA = 6 for each segment! This treats it like a hexagon instead of a rectangle. The middle line BE divides the rectangle but isn't part of the perimeter. Always identify the outer boundary: length = 12, width = 6, so perimeter = 2(12) + 2(6) = 36.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

Why isn't the middle line part of the perimeter?

The perimeter is only the outer boundary of a shape. The line BE just shows how the rectangle is made of two squares - it's inside the rectangle, not around it!

How do I know the rectangle's length and width?

Since each square has side length 6, the rectangle's length is two squares side-by-side: 6 + 6 = 12. The width is just one square's side: 6.

Can I use the square perimeter formula instead?

No! This is a rectangle, not a square. Use the rectangle formula: $P = 2l + 2w$ where length = 12 and width = 6.

What if I counted 6 sides and got 36?

That's accidentally correct but for the wrong reason! You're counting internal segments. The proper method is rectangle perimeter formula: $2 \times 12 + 2 \times 6 = 36$ .

How do I verify my answer is correct?

Check that your perimeter makes sense: you should go around the outside edge once. Count: top edge (12) + right edge (6) + bottom edge (12) + left edge (6) = 36 ✓

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