Calculate Rectangle Perimeter: Finding ABCD with Measurements 8, 5, and 3

Q: Why is AB equal to 11 and not 8?

Because AB is the entire top side of rectangle ABCD! It consists of two parts: AE (which is 8) plus EB (which is 3). So AB = 8 + 3 = 11.

Q: What does it mean that ABCD and EBFC are both rectangles?

It means both shapes follow rectangle rules: opposite sides are equal and all angles are 90°. Rectangle EBFC is inside rectangle ABCD, sharing some sides.

Q: Can I solve this problem if the rectangles weren't overlapping?

No! The overlapping arrangement is crucial because it lets us use the measurements from the smaller rectangle to find the missing dimensions of the larger rectangle ABCD.

Rectangle Perimeter with Overlapping Shapes

ABCD and EBFC are rectangles.

Calculate the perimeter of rectangle ABCD.

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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

00:25 The whole side equals the sum of its parts

00:36 Opposite sides are equal in a rectangle

00:46 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

Understand the problem

ABCD and EBFC are rectangles.

Calculate the perimeter of rectangle ABCD.

Step-by-step solution

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

$EF=BC=AD=5$

$FC=EB=3$

Now we can calculate side AB:

$8+3=11$

Since AB and CD are equal to each other, side CD is also equal to 11

Let's calculate the perimeter of the rectangle:

$11+5+11+5=22+10=32$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Properties: Opposite sides are equal in length
Technique: AB = AE + EB = 8 + 3 = 11
Check: Perimeter = 2(length + width) = 2(11 + 5) = 32 ✓

Common Mistakes

Avoid these frequent errors

Using only the given measurements without finding missing sides
Don't just add 8 + 5 + 3 = 16 and assume that's the perimeter! This ignores that rectangles have four sides with opposite sides equal. Always find all four side lengths: AB = 11, BC = 5, CD = 11, DA = 5.

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 measurements belong to which rectangle?

Look at the diagram carefully! The 8 is marked along side AE, the 5 is marked along the vertical line EF (which equals BC and AD), and the 3 is marked along side FC (which equals EB).

Why is AB equal to 11 and not 8?

Because AB is the entire top side of rectangle ABCD! It consists of two parts: AE (which is 8) plus EB (which is 3). So AB = 8 + 3 = 11.

What does it mean that ABCD and EBFC are both rectangles?

It means both shapes follow rectangle rules: opposite sides are equal and all angles are 90°. Rectangle EBFC is inside rectangle ABCD, sharing some sides.

How do I find the perimeter once I know all sides?

Add all four sides: AB + BC + CD + DA = 11 + 5 + 11 + 5 = 32. Or use the formula: $P = 2(length + width) = 2(11 + 5) = 32$

Can I solve this problem if the rectangles weren't overlapping?

No! The overlapping arrangement is crucial because it lets us use the measurements from the smaller rectangle to find the missing dimensions of the larger rectangle ABCD.

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