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

Question

Look at the two rectangles in the figure:

222444555222EEEDDDGGGFFFCCCBBBAAA

What is the area of the white area?

Video Solution

Solution Steps

00:00 Find the area of the white region
00:03 Let's start by calculating the area of rectangle EFGD
00:07 We'll use the formula for calculating rectangle area
00:10 Side(2) multiplied by side(4)
00:13 Now let's calculate the area of 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 let's 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 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

Answer

28 cm²