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

Look at the two rectangles in the figure:

222444555222EEEDDDGGGFFFCCCBBBAAA

What is the area of the white area?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

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

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Rectangles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations