Calculate Rectangle Perimeter: Finding the Distance Around ABCD with Dimensions 6, 4, and 3

Q: Why can't I just add all the numbers I see?

The diagram shows interior divisions within the rectangle, not just the outer boundary. You need to combine segments that make up each complete side before calculating perimeter.

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

Look at the rectangle's vertices (A, B, C, D). Side AB goes from point A to point B, which includes segments AG, GH, and HB all in one straight line.

Q: How can I verify my rectangle dimensions are correct?

Check that opposite sides are equal: AB should equal DC, and AD should equal BC. If they match, you've correctly identified the rectangle's dimensions!

Rectangle Perimeter with Composite Measurements

Determine the perimeter of the rectangle ABCD?

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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 rectangle ABCD

00:04 Opposite sides are equal in the rectangle JHBC

00:15 Opposite sides are equal in the rectangle AGDI

00:25 Opposite sides are equal in the rectangle FECD

00:42 Opposite sides are equal in the rectangle AFBE

00:48 Opposite sides are equal in the rectangle GHIJ

00:58 The whole side equals the sum of its parts

01:12 Opposite sides are equal in the rectangle ABCD

01:16 The whole side equals the sum of its parts

01:19 The perimeter of the rectangle equals the sum of its sides

01:29 Substitute in the relevant values and proceed to solve for the perimeter

01:51 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine the perimeter of the rectangle ABCD?

Step-by-step solution

According to the given data:

$JC=HB=3$

$DI=AG=3$

$FD=EC=3$

$BE=AF=4$

$GH=JI=6$

Now we can calculate sides AB and DC

$3+6+3=9+3=12$

And also sides AD and BC

$4+3=7$

Now we can calculate the perimeter of rectangle ABCD:

$12+7+12+7=24+14=38$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: Opposite sides are equal in length
Technique: Add segments: AB = AG + GH + HB = 3 + 6 + 3 = 12
Check: Verify perimeter formula: 2(length + width) = 2(12 + 7) = 38 ✓

Common Mistakes

Avoid these frequent errors

Adding all visible measurements directly
Don't add all labeled segments like 6 + 4 + 3 + 3 + 3 = 19 and double it = wrong answer! This counts interior segments that aren't part of the rectangle's boundary. Always identify which segments form the actual rectangle sides first.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why can't I just add all the numbers I see?

The diagram shows interior divisions within the rectangle, not just the outer boundary. You need to combine segments that make up each complete side before calculating perimeter.

How do I know which segments belong to each side?

Look at the rectangle's vertices (A, B, C, D). Side AB goes from point A to point B, which includes segments AG, GH, and HB all in one straight line.

What if the segments don't seem to add up correctly?

Double-check that you're reading the diagram correctly. Each colored segment represents a different measurement, and segments of the same color should have equal lengths.

Is there a shortcut to avoid adding all these segments?

Unfortunately, no! When a rectangle is divided into segments, you must carefully add the segments that form each complete side. This builds important spatial reasoning skills.

How can I verify my rectangle dimensions are correct?

Check that opposite sides are equal: AB should equal DC, and AD should equal BC. If they match, you've correctly identified the rectangle's dimensions!

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