Calculate the White Area: Rectangle Geometry with 2×4 and 5-Unit Dimensions

Rectangle Area Calculation with Overlapping Regions

Look at the two rectangles in the figure:

222444555222EEEDDDGGGFFFCCCBBBAAA

What is the area of the white area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the area of the white region
00:03 Start by calculating the area of the rectangle EFGD
00:07 Apply the formula for calculating the area of the rectangle
00:10 Side(2) multiplied by side(4)
00:13 Proceed to calculate the area of the rectangle ABCD
00:21 Each side equals the sum of its parts(2+2)
00:24 The same happens with side DC (4+5)
00:27 This is the area of rectangle ABCD
00:31 Now subtract the area of the smaller rectangle from the larger one
00:35 This is the size of the white area and the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the two rectangles in the figure:

222444555222EEEDDDGGGFFFCCCBBBAAA

What is the area of the white area?

2

Step-by-step solution

As we know that EFGD is a rectangle, we also know that DE is equal to 2 and DG is equal to 4

In a rectangle, each pair of opposite sides are equal and parallel, therefore:

ED=FG=2 ED=FG=2

DG=EF=4 DG=EF=4

Now we calculate the area of the orange rectangle EFGD by multiplying the length by the width:

2×4=8 2\times4=8

Now we calculate the total area of the white rectangle ABCD:

AD=AE+ED=2+2=4 AD=AE+ED=2+2=4

DC=DG+GC=4+5=9 DC=DG+GC=4+5=9

The area of the entire rectangle ABCD is:

4×9=36 4\times9=36

Now to find the area of the white part that is not covered by the area of the orange rectangle, we will subtract the area of the rectangle EFGD from the rectangle ABCD:

368=28 36-8=28

3

Final Answer

28 cm²

Key Points to Remember

Essential concepts to master this topic
  • Total Area Rule: Large rectangle area equals length times width
  • Subtraction Technique: White area = Total area - Orange area = 36 - 8
  • Verification Check: Confirm dimensions add correctly: AD = 2+2 = 4, DC = 4+5 = 9 ✓

Common Mistakes

Avoid these frequent errors
  • Only calculating the orange rectangle area
    Don't just find the area of rectangle EFGD (2×4 = 8) and stop there! This gives you the covered area, not the white area requested. Always subtract the orange area from the total rectangle area to find the remaining white space.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?
222777AAABBBCCCDDD

FAQ

Everything you need to know about this question

Why do I need to find the total rectangle area first?

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The white area is what's left over after removing the orange rectangle. You need the total area of rectangle ABCD to subtract the orange area from it.

How do I know which dimensions to add together?

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Look at the figure carefully! AD = AE + ED = 2 + 2 = 4, and DC = DG + GC = 4 + 5 = 9. Add segments that lie on the same side.

What if I calculated the orange area wrong?

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Double-check that rectangle EFGD has dimensions 2 × 4. In rectangles, opposite sides are equal, so ED = FG = 2 and DG = EF = 4.

Can I solve this without subtraction?

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You could break the white area into smaller rectangles, but subtraction is much easier! Total area minus covered area always gives the remaining area.

How do I verify my final answer is correct?

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Check that 28+8=36 28 + 8 = 36 . The white area plus orange area should equal the total rectangle area. If they don't add up, recheck your calculations!

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