A room 9.5 m long and 6 m wide is surrounded by a 1.25-m-wide verandah. Calculate the cost of cementing the floor of this verandah atRs.  80 per `m^(2)`. 

Answer

To solve the problem step by step, follow the instructions below:

### Step 1: Calculate the area of the room.
The room is a rectangle with a length of 9.5 m and a width of 6 m. The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{width} \]
Substituting the values:
\[ A = 9.5 \, \text{m} \times 6 \, \text{m} = 57 \, \text{m}^2 \]

### Step 2: Calculate the dimensions of the verandah.
The verandah surrounds the room and is 1.25 m wide. Therefore, the total length and width of the area including the verandah can be calculated as follows:
- Total length of the area (room + verandah) = Room length + 2 × Verandah width
\[ \text{Total length} = 9.5 \, \text{m} + 2 \times 1.25 \, \text{m} = 9.5 \, \text{m} + 2.5 \, \text{m} = 12 \, \text{m} \]
- Total width of the area (room + verandah) = Room width + 2 × Verandah width
\[ \text{Total width} = 6 \, \text{m} + 2 \times 1.25 \, \text{m} = 6 \, \text{m} + 2.5 \, \text{m} = 8.5 \, \text{m} \]

### Step 3: Calculate the area of the verandah.
Now, we can calculate the area of the entire space (room + verandah) using the total dimensions found in Step 2:
\[ \text{Area of the entire space} = \text{Total length} \times \text{Total width} \]
\[ \text{Area of the entire space} = 12 \, \text{m} \times 8.5 \, \text{m} = 102 \, \text{m}^2 \]

Now, to find the area of the verandah, subtract the area of the room from the area of the entire space:
\[ \text{Area of the verandah} = \text{Area of the entire space} - \text{Area of the room} \]
\[ \text{Area of the verandah} = 102 \, \text{m}^2 - 57 \, \text{m}^2 = 45 \, \text{m}^2 \]

### Step 4: Calculate the cost of cementing the verandah.
The cost of cementing is given as Rs. 80 per square meter. Therefore, the total cost can be calculated by multiplying the area of the verandah by the cost per square meter:
\[ \text{Total cost} = \text{Area of the verandah} \times \text{Cost per square meter} \]
\[ \text{Total cost} = 45 \, \text{m}^2 \times 80 \, \text{Rs/m}^2 = 3600 \, \text{Rs} \]

### Final Answer:
The total cost of cementing the floor of the verandah is **Rs. 3600**.

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