Calculate Rectangle Perimeter: Adding 3, 4, 5, and 7 Unit Segments

Q: How do I know which segments belong to which side?

Look at the colored segments in the diagram! Segments that are connected along the same edge of the rectangle combine to form one complete side.

Q: Why are there extra points inside the rectangle?

The points E, F, G, H create internal divisions that help measure the rectangle's dimensions. They show how each side is broken into smaller, measurable segments.

Q: Do I add all four numbers together?

No! Don't add 3+4+5+7 directly. Instead, identify which segments form complete sides: $ AD = 5+3 = 8 $ and $ AB = 7+4 = 11 $

Q: How do I calculate the perimeter once I know the sides?

Use the formula Perimeter = 2(length + width). With sides 8 and 11: $ P = 2(8+11) = 2(19) = 38 $

Q: What if the segments don't add up correctly?

Check your diagram interpretation! Make sure you're reading the colored segments correctly and matching them to the proper rectangle sides.

Rectangle Perimeter with Segmented Dimensions

What is the perimeter of the given rectangle ABCD?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

00:10 Remember, in a rectangle, opposite sides are equal. For example, sides F E, and C D, are the same.

00:34 Also, in another example, sides A G, and D H, are equal too.

00:43 You can think of the whole side as being equal to the sum of its parts.

00:56 In rectangle ABCD, opposite sides are once again equal.

01:02 To find the perimeter, just add up all the sides together.

01:11 Now, substitute the given values into the formula, and solve for the perimeter.

01:31 And there you have it, that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the perimeter of the given rectangle ABCD?

Step-by-step solution

According to the data let's consider:

$CF=DE=3$

$AE=BF=5$

Now we can calculate BC:

$5+3=8$

$AD=BC=8$

Next we pay attention to any additional information and it seems that:

$GB=HC=4$

$DH=AG=7$

Hence we can calculate AB:

$7+4=11$

$AB=DC=11$

Lastly we can calculate the perimeter of the rectangle ABCD:

$8+8+11+11=$

$16+22=38$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: Opposite sides are equal in length
Technique: Add segments to find side length: $5+3=8$ and $7+4=11$
Check: Perimeter formula $2(l+w) = 2(8+11) = 38$ ✓

Common Mistakes

Avoid these frequent errors

Not recognizing that sides are divided into segments
Don't just count the individual segments 3, 4, 5, 7 = wrong answer 19! This ignores that segments combine to form complete rectangle sides. Always identify which segments form each side: AE+EC = 5+3 = 8 and AG+GB = 7+4 = 11.

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

How do I know which segments belong to which side?

Look at the colored segments in the diagram! Segments that are connected along the same edge of the rectangle combine to form one complete side.

Why are there extra points inside the rectangle?

The points E, F, G, H create internal divisions that help measure the rectangle's dimensions. They show how each side is broken into smaller, measurable segments.

Do I add all four numbers together?

No! Don't add 3+4+5+7 directly. Instead, identify which segments form complete sides: $AD = 5+3 = 8$ and $AB = 7+4 = 11$

How do I calculate the perimeter once I know the sides?

Use the formula Perimeter = 2(length + width). With sides 8 and 11: $P = 2(8+11) = 2(19) = 38$

What if the segments don't add up correctly?

Check your diagram interpretation! Make sure you're reading the colored segments correctly and matching them to the proper rectangle sides.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Rectangles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime