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### Mathematical Literacy Grade 12
Preparatory Test

QUESTION 4 [13]

The following is a floor plan of a three-bedroom house:

- Bathroom: [tex]1.5 \, \text{m} \times 2.5 \, \text{m}[/tex]
- Toilet: [tex]1.3 \, \text{m} \times 2.5 \, \text{m}[/tex]
- Lounge: [tex]2.7 \, \text{m} \times 5 \, \text{m}[/tex]
- Bedroom 1: [tex]3.5 \, \text{m} \times 3.7 \, \text{m}[/tex]
- Bedroom 2: [tex]3.5 \, \text{m} \times 4.6 \, \text{m}[/tex]
- Bedroom 3: [tex]5 \, \text{m} \times 3.2 \, \text{m}[/tex]

- Area of cupboards in kitchen: [tex]2.7 \, \text{m}^2[/tex]
- Area covered by stove: [tex]0.45 \, \text{m}^2[/tex]
- Sink: [tex]500 \, \text{mm} \times 1.2 \, \text{m}[/tex]

Determine:

4.1 The total floor area (in [tex]\text{m}^2[/tex]) if the owner wishes to tile the kitchen, dining room, and lounge (considering that no tiles are to be placed under the cupboards, sink, and stove).
(6)

4.2 The number of tiles needed if each tile has dimensions [tex]30 \, \text{cm} \times 30 \, \text{cm}[/tex].
(5)

4.3 Write down the name(s) of the room(s) of which the door(s) is/are facing east.
(2)

END OF QUESTION 4



Answer :

GinnyAnswer
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

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