Answer:
[tex]Area = 49\frac{25}{36}[/tex]
Step-by-step explanation:
Given
Tile
[tex]Length = 4\frac{5}{6}[/tex]
[tex]Width = 2\frac{1}{3}[/tex]
See attachment for dimension of the floor
Required
Determine the area covered by the carpet
From the attachment, the dimension of the floor is:
[tex]Length = 12\frac{1}{4}[/tex]
[tex]Width = 5[/tex]
Calculate Area
[tex]Area = Length * Width[/tex]
[tex]Area = 12\frac{1}{4} * 5[/tex]
[tex]Area = 61\frac{1}{4}[/tex]
The area of the tiles is:
[tex]Area = 4\frac{5}{6} * 2\frac{1}{3}[/tex]
[tex]Area = \frac{29}{6} * \frac{7}{3}[/tex]
[tex]Area = \frac{203}{18}[/tex]
[tex]Area = 11\frac{5}{18}[/tex]
So, the carpet area is:
[tex]Area = Floor\ Area - Tile\ Area[/tex]
[tex]Area = 61\frac{1}{4} - 11\frac{5}{18}[/tex]
To improper number
[tex]Area = \frac{245}{4} - \frac{208}{18}[/tex]
Take LCM
[tex]Area = \frac{2205 - 416}{36}[/tex]
[tex]Area = \frac{1789}{36}[/tex]
[tex]Area = 49\frac{25}{36}[/tex]
