Certainly! Let's work through each part of the question step-by-step.
### Part (a)(i): Find the area of the floor
The area of a rectangle is given by the formula:
[tex]\[ \text{Area} = \text{length} \times \text{breadth} \][/tex]
Given length [tex]\( = 12 \, \text{meters} \)[/tex] and breadth [tex]\( = 8 \, \text{meters} \)[/tex]:
[tex]\[ \text{Area of the floor} = 12 \, \text{m} \times 8 \, \text{m} = 96 \, \text{square meters} \][/tex]
So, the area of the floor is [tex]\( 96 \, \text{m}^2 \)[/tex].
### Part (a)(ii): Find the area of the ceiling if the room is rectangular
In the case of a rectangular room, the ceiling is directly above the floor and has the same dimensions as the floor. Therefore:
[tex]\[ \text{Area of the ceiling} = \text{Area of the floor} \][/tex]
From part (i), we know:
[tex]\[ \text{Area of the ceiling} = 96 \, \text{m}^2 \][/tex]
So, the area of the ceiling is also [tex]\( 96 \, \text{m}^2 \)[/tex].
### Part (a)(iii): How many square tiles will be needed to cover the floor if the side of the tile is 60 cm?
First, we need to convert the side of each tile from centimeters to meters to match the units of the floor's area calculations.
[tex]\[ 60 \, \text{cm} = 60 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 0.6 \, \text{m} \][/tex]
Next, calculate the area of one square tile:
[tex]\[ \text{Area of one tile} = \text{side} \times \text{side} = 0.6 \, \text{m} \times 0.6 \, \text{m} = 0.36 \, \text{m}^2 \][/tex]
To find out how many such tiles are needed to cover the floor, we divide the area of the floor by the area of one tile:
[tex]\[ \text{Number of tiles needed} = \frac{\text{Area of the floor}}{\text{Area of one tile}} = \frac{96 \, \text{m}^2}{0.36 \, \text{m}^2} \][/tex]
[tex]\[ \text{Number of tiles needed} = \frac{96}{0.36} \approx 266.67 \][/tex]
Since we cannot have a fraction of a tile in this context, we will need to round up to ensure the entire floor is covered. Thus, we need:
[tex]\[ \lceil 266.67 \rceil = 267 \][/tex]
So, 267 tiles will be needed to cover the floor.
### Summary:
- The area of the floor is [tex]\( 96 \, \text{m}^2 \)[/tex].
- The area of the ceiling is [tex]\( 96 \, \text{m}^2 \)[/tex].
- The number of square tiles needed to cover the floor is 267.
