Calculate the Perimeter: Rectangle ABCD with Three Internal Subdivisions

Rectangle Perimeter with Internal Subdivisions

Rectangle ABCD contains three other rectangles inside it.

Calculate the perimeter of ABCD.

AAABBBCCCDDDEEEFFFGGGHHH975

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perimeter of rectangle ABCD
00:03 Opposite sides are equal in a rectangle
00:11 The whole side equals the sum of its parts
00:17 Opposite sides are equal in a rectangle
00:36 The perimeter of the rectangle equals the sum of its sides
01:01 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Rectangle ABCD contains three other rectangles inside it.

Calculate the perimeter of ABCD.

AAABBBCCCDDDEEEFFFGGGHHH975

2

Step-by-step solution

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

GH=AE=DF=9 GH=AE=DF=9

Now we can calculate side CD:

9+5=14 9+5=14

Since side CD is equal to side AB, it is also equal to 14

BC=AD=7 BC=AD=7

Let's calculate the perimeter of rectangle ABCD:

7+14+7+14=14+28=42 7+14+7+14=14+28=42

3

Final Answer

42

Key Points to Remember

Essential concepts to master this topic
  • Rectangle Property: Opposite sides are equal in length
  • Technique: Add segments: CD = CF + FD = 9 + 5 = 14
  • Check: Perimeter = 2(length + width) = 2(14 + 7) = 42 ✓

Common Mistakes

Avoid these frequent errors
  • Using only the given measurements without finding complete side lengths
    Don't just add 9 + 7 + 5 = 21 and call it the perimeter! This ignores that rectangles have four sides and opposite sides are equal. Always find the complete length and width first, then calculate 2(length + width).

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?
666444AAABBBCCCDDD

FAQ

Everything you need to know about this question

How do I know which segments add up to make a complete side?

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Look at the diagram carefully! Side CD is divided into two parts: CF (which equals 9) and FD (which equals 5). So CD = CF + FD = 9 + 5 = 14.

Why can I say that AE = GH = 9?

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In a rectangle, opposite sides are equal and parallel lines cut by parallel lines create equal segments. Since the internal rectangles align perfectly, corresponding segments are equal.

What if I can't see all the measurements clearly?

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Use the rectangle property! Once you find one complete side length, the opposite side has the same length. You only need to find the length and width to calculate the perimeter.

Is there a formula I should memorize?

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Yes! For any rectangle: Perimeter = 2(length + width). The key is correctly identifying what the full length and width are from the given segments.

How do I check if my perimeter is reasonable?

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Your perimeter should be greater than twice the longest measurement you can see. In this case, since we see 9, 7, and 5, a perimeter of 42 makes sense!

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