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Sagot :
Let's solve the problem step-by-step as requested.
### 4.1 The Total Floor Area to be Tiled
First, we need to consider the floor dimensions as given and calculate the areas of each room.
- Bathroom Area:
[tex]\[ \text{Bathroom Area} = 1.5\,m \times 2.5\,m = 3.75\,m^2 \][/tex]
- Toilet Area:
[tex]\[ \text{Toilet Area} = 1.3\,m \times 2.5\,m = 3.25\,m^2 \][/tex]
- Lounge Area:
[tex]\[ \text{Lounge Area} = 2.7\,m \times 5\,m = 13.5\,m^2 \][/tex]
- Bedroom 1 Area:
[tex]\[ \text{Bedroom 1 Area} = 3.5\,m \times 3.7\,m = 12.95\,m^2 \][/tex]
- Bedroom 2 Area:
[tex]\[ \text{Bedroom 2 Area} = 3.5\,m \times 4.6\,m = 16.1\,m^2 \][/tex]
- Bedroom 3 Area:
[tex]\[ \text{Bedroom 3 Area} = 5\,m \times 3.2\,m = 16.0\,m^2 \][/tex]
Next, we have certain areas within the kitchen that should not be tiled:
- Area of Cupboards: 2.7 m²
- Area Covered by Stove: 0.45 m²
The sink's dimensions are given in millimeters for one side, so let's convert this:
- Sink Dimensions:
[tex]\[ \text{Sink Length} = 500\,mm = 0.5\,m \][/tex]
- Sink Area:
[tex]\[ \text{Sink Area} = 0.5\,m \times 1.2\,m = 0.6\,m^2 \][/tex]
The next step is to exclude the areas of the cupboards, stove, and sink from the lounge area:
[tex]\[ \text{Total Floor Area to be Tiled} = \text{Lounge Area} - \text{Cupboards Area} - \text{Stove Area} - \text{Sink Area} \][/tex]
[tex]\[ \text{Total Floor Area to be Tiled} = 13.5\,m^2 - 2.7\,m^2 - 0.45\,m^2 - 0.6\,m^2 = 9.75\,m^2 \][/tex]
Thus, the total floor area to be tiled is [tex]\(9.75\,m^2\)[/tex].
### 4.2 The Number of Tiles Needed
Next, we need to calculate the number of tiles required. Each tile has dimensions [tex]\(30\,cm \times 30\,cm\)[/tex]. Converting these dimensions to meters:
[tex]\[ 30\,cm = 0.3\,m \][/tex]
- Tile Area:
[tex]\[ \text{Tile Area} = 0.3\,m \times 0.3\,m = 0.09\,m^2 \][/tex]
To find the number of tiles:
[tex]\[ \text{Number of Tiles Needed} = \frac{\text{Total Floor Area to be Tiled}}{\text{Tile Area}} \][/tex]
[tex]\[ \text{Number of Tiles Needed} = \frac{9.75\,m^2}{0.09\,m^2} = 108.33 \][/tex]
Since we cannot have a fraction of a tile, we would typically round up to ensure we have enough tiles. Thus, [tex]\(109\)[/tex] tiles will be needed.
### 4.3 Rooms with Doors Facing East
Assuming that from given positions, the room(s) with doors facing east is listed, we get:
- Rooms with Doors Facing East:
- Lounge
So, the name of the room with its door facing east is "Lounge".
### Final Answer Summary:
- 4.1 Total Floor Area to be Tiled: [tex]\(9.75\,m^2\)[/tex]
- 4.2 Number of Tiles Needed: [tex]\(109\)[/tex]
- 4.3 Rooms with Doors Facing East: Lounge
### 4.1 The Total Floor Area to be Tiled
First, we need to consider the floor dimensions as given and calculate the areas of each room.
- Bathroom Area:
[tex]\[ \text{Bathroom Area} = 1.5\,m \times 2.5\,m = 3.75\,m^2 \][/tex]
- Toilet Area:
[tex]\[ \text{Toilet Area} = 1.3\,m \times 2.5\,m = 3.25\,m^2 \][/tex]
- Lounge Area:
[tex]\[ \text{Lounge Area} = 2.7\,m \times 5\,m = 13.5\,m^2 \][/tex]
- Bedroom 1 Area:
[tex]\[ \text{Bedroom 1 Area} = 3.5\,m \times 3.7\,m = 12.95\,m^2 \][/tex]
- Bedroom 2 Area:
[tex]\[ \text{Bedroom 2 Area} = 3.5\,m \times 4.6\,m = 16.1\,m^2 \][/tex]
- Bedroom 3 Area:
[tex]\[ \text{Bedroom 3 Area} = 5\,m \times 3.2\,m = 16.0\,m^2 \][/tex]
Next, we have certain areas within the kitchen that should not be tiled:
- Area of Cupboards: 2.7 m²
- Area Covered by Stove: 0.45 m²
The sink's dimensions are given in millimeters for one side, so let's convert this:
- Sink Dimensions:
[tex]\[ \text{Sink Length} = 500\,mm = 0.5\,m \][/tex]
- Sink Area:
[tex]\[ \text{Sink Area} = 0.5\,m \times 1.2\,m = 0.6\,m^2 \][/tex]
The next step is to exclude the areas of the cupboards, stove, and sink from the lounge area:
[tex]\[ \text{Total Floor Area to be Tiled} = \text{Lounge Area} - \text{Cupboards Area} - \text{Stove Area} - \text{Sink Area} \][/tex]
[tex]\[ \text{Total Floor Area to be Tiled} = 13.5\,m^2 - 2.7\,m^2 - 0.45\,m^2 - 0.6\,m^2 = 9.75\,m^2 \][/tex]
Thus, the total floor area to be tiled is [tex]\(9.75\,m^2\)[/tex].
### 4.2 The Number of Tiles Needed
Next, we need to calculate the number of tiles required. Each tile has dimensions [tex]\(30\,cm \times 30\,cm\)[/tex]. Converting these dimensions to meters:
[tex]\[ 30\,cm = 0.3\,m \][/tex]
- Tile Area:
[tex]\[ \text{Tile Area} = 0.3\,m \times 0.3\,m = 0.09\,m^2 \][/tex]
To find the number of tiles:
[tex]\[ \text{Number of Tiles Needed} = \frac{\text{Total Floor Area to be Tiled}}{\text{Tile Area}} \][/tex]
[tex]\[ \text{Number of Tiles Needed} = \frac{9.75\,m^2}{0.09\,m^2} = 108.33 \][/tex]
Since we cannot have a fraction of a tile, we would typically round up to ensure we have enough tiles. Thus, [tex]\(109\)[/tex] tiles will be needed.
### 4.3 Rooms with Doors Facing East
Assuming that from given positions, the room(s) with doors facing east is listed, we get:
- Rooms with Doors Facing East:
- Lounge
So, the name of the room with its door facing east is "Lounge".
### Final Answer Summary:
- 4.1 Total Floor Area to be Tiled: [tex]\(9.75\,m^2\)[/tex]
- 4.2 Number of Tiles Needed: [tex]\(109\)[/tex]
- 4.3 Rooms with Doors Facing East: Lounge
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