Calculate Rectangle Perimeter: Finding ABFE Using 4, 5, and 10 Units

Q: How do I know which numbers represent full sides versus segments?

Look at the diagram carefully! The numbers 4, 5, 8, and 10 are placed on parts of the sides, not the complete sides. Use rectangle properties to find the full side lengths.

Q: Why isn't the perimeter just 4 + 5 + 8 + 10?

Those numbers represent segments within the rectangle, not the complete sides of rectangle ABFE. You need to calculate the actual side lengths AB and AE first.

Q: How do I find the length of side AE?

Since BC = 10 (the full height) and ED = 4, then $ AE = BC - ED = 10 - 4 = 6 $. Remember that in rectangles, opposite sides are equal!

Q: What's the relationship between all these labeled points?

Points A, B, C, D form the outer rectangle, while E and F are interior points that create rectangle ABFE. Use the given measurements to find where these points divide the sides.

Q: How can I check if my perimeter calculation is correct?

Verify that opposite sides are equal: AB should equal EF, and AE should equal BF. If $ AB = EF = 13 $ and $ AE = BF = 6 $, then your perimeter $ 13 + 6 + 13 + 6 = 38 $ is correct!

Rectangle Perimeter with Given Side Segments

Look at the following rectangle:

What is the perimeter of the rectangle ABFE?

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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 rectangle A-B-F-E. Ready?

00:12 In rectangle G-B-H-C, remember! Opposite sides are the same length.

00:25 For rectangle E-D-F-C, opposite sides are equal too. That's important!

00:36 Segment B-E is the whole side B-C minus segment F-C. You got this!

00:44 Rectangle A-B-E-F also has opposite sides that are equal.

00:52 The entire side is just the sum of its parts. Simple, right?

00:59 In rectangle A-B-C-D, opposite sides are equal once more.

01:09 To find the perimeter, add up all the sides. Easy peasy!

01:21 Now, put the correct numbers into the formula and calculate the perimeter.

01:48 And there you have it! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following rectangle:

What is the perimeter of the rectangle ABFE?

Step-by-step solution

Based on the given data, we can claim that:

$HC=GB=8$

$ED=FC=4$

$AE=BC=10$

Now we can calculate side AE:

$AE=10-4=6$

$AE=BF=6$

Now we can calculate side AB which is equal to side CD:

$AB=CD=EF=8+5=13$

Now we can calculate the perimeter of rectangle ABFE:

$13+6+13+6=26+12=38$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Properties: Opposite sides are equal and parallel in rectangles
Segment Addition: Calculate full sides by adding or subtracting given segments like $AB = AG + GB = 5 + 8 = 13$
Perimeter Check: Add all four sides: $P = 13 + 6 + 13 + 6 = 38$ ✓

Common Mistakes

Avoid these frequent errors

Using given measurements directly as full side lengths
Don't assume the numbers 4, 5, 8, and 10 are the rectangle's full side lengths = wrong perimeter of 54! These are partial segments within the rectangle. Always identify which measurements represent complete sides versus partial segments by analyzing the diagram carefully.

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 numbers represent full sides versus segments?

Look at the diagram carefully! The numbers 4, 5, 8, and 10 are placed on parts of the sides, not the complete sides. Use rectangle properties to find the full side lengths.

Why isn't the perimeter just 4 + 5 + 8 + 10?

Those numbers represent segments within the rectangle, not the complete sides of rectangle ABFE. You need to calculate the actual side lengths AB and AE first.

How do I find the length of side AE?

Since BC = 10 (the full height) and ED = 4, then $AE = BC - ED = 10 - 4 = 6$ . Remember that in rectangles, opposite sides are equal!

What's the relationship between all these labeled points?

Points A, B, C, D form the outer rectangle, while E and F are interior points that create rectangle ABFE. Use the given measurements to find where these points divide the sides.

How can I check if my perimeter calculation is correct?

Verify that opposite sides are equal: AB should equal EF, and AE should equal BF. If $AB = EF = 13$ and $AE = BF = 6$ , then your perimeter $13 + 6 + 13 + 6 = 38$ is correct!

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