Let's solve this problem step-by-step.
### Step 1: Floor Area Calculation
The room is square-shaped with a length of 15 feet.
[tex]\[ \text{Area of the floor} = \text{length} \times \text{length} \][/tex]
[tex]\[ \text{Area of the floor} = 15 \, \text{ft} \times 15 \, \text{ft} = 225 \, \text{sq ft} \][/tex]
### Step 2: Ceiling Area Calculation
Since the ceiling is also square-shaped with the same dimensions as the floor:
[tex]\[ \text{Area of the ceiling} = 15 \, \text{ft} \times 15 \, \text{ft} = 225 \, \text{sq ft} \][/tex]
### Step 3: Wall Area Calculation
The room has four walls, and we consider two pairs of opposite walls.
#### Calculation for one pair of opposite walls:
Each wall in this pair has a length of 15 feet and a height of 8 feet.
[tex]\[ \text{Area of one wall} = \text{length} \times \text{height} \][/tex]
[tex]\[ \text{Area of one wall} = 15 \, \text{ft} \times 8 \, \text{ft} = 120 \, \text{sq ft} \][/tex]
Since there are two such walls:
[tex]\[ \text{Total area for this pair} = 2 \times 120 \, \text{sq ft} = 240 \, \text{sq ft} \][/tex]
#### Calculation for the other pair of opposite walls:
Since the room is square, the second pair of opposite walls will have the same dimensions and area as the first pair.
[tex]\[ \text{Total area for this pair} = 2 \times 120 \, \text{sq ft} = 240 \, \text{sq ft} \][/tex]
### Step 4: Total Wall Area Calculation
Now, we add up the areas of the four walls:
[tex]\[ \text{Total wall area} = 240 \, \text{sq ft} + 240 \, \text{sq ft} = 480 \, \text{sq ft} \][/tex]
### Step 5: Total Area to be Plastered
We now sum the areas of the floor, ceiling, and all four walls:
[tex]\[ \text{Total area} = \text{Area of the floor} + \text{Area of the ceiling} + \text{Total wall area} \][/tex]
[tex]\[ \text{Total area} = 225 \, \text{sq ft} + 225 \, \text{sq ft} + 480 \, \text{sq ft} = 930 \, \text{sq ft} \][/tex]
### Step 6: Cost Calculation
The rate of plastering is 120 per square foot.
[tex]\[ \text{Total cost} = \text{Total area} \times \text{cost per sq ft} \][/tex]
[tex]\[ \text{Total cost} = 930 \, \text{sq ft} \times 120 \, \text{per sq ft} = 111600 \][/tex]
### Final Answer:
The total cost to plaster the floor, four walls, and ceiling of the room is 111,600.
