To solve the problem step by step, we need to follow these steps:
### Step 1: Calculate the area of the hall
The area of the hall can be calculated using the formula:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
Given:
- Length of the hall = 37.5 m
- Width of the hall = 11.2 m
Calculating the area:
\[
\text{Area} = 37.5 \, \text{m} \times 11.2 \, \text{m} = 420 \, \text{m}^2
\]
### Step 2: Convert the area of the hall to square centimeters
Since the size of the tiles is given in centimeters, we need to convert the area of the hall from square meters to square centimeters.
1 square meter = 10,000 square centimeters.
Calculating the area in square centimeters:
\[
\text{Area in cm}^2 = 420 \, \text{m}^2 \times 10,000 \, \text{cm}^2/\text{m}^2 = 4,200,000 \, \text{cm}^2
\]
### Step 3: Calculate the area of one tile
The area of one rectangular tile can be calculated using the formula:
\[
\text{Area of tile} = \text{Length of tile} \times \text{Width of tile}
\]
Given:
- Length of tile = 15 cm
- Width of tile = 7 cm
Calculating the area of one tile:
\[
\text{Area of tile} = 15 \, \text{cm} \times 7 \, \text{cm} = 105 \, \text{cm}^2
\]
### Step 4: Calculate the number of tiles required
To find the number of tiles needed, we divide the total area of the hall by the area of one tile:
\[
\text{Number of tiles} = \frac{\text{Area of hall}}{\text{Area of one tile}} = \frac{4,200,000 \, \text{cm}^2}{105 \, \text{cm}^2} \approx 40,000
\]
### Step 5: Calculate the total cost of tiling
The total cost can be calculated by multiplying the number of tiles by the cost per tile:
\[
\text{Total cost} = \text{Number of tiles} \times \text{Cost per tile}
\]
Given:
- Cost per tile = Rs 1.25
Calculating the total cost:
\[
\text{Total cost} = 40,000 \times 1.25 = 50,000 \, \text{Rs}
\]
### Final Answer
The total cost of tiling the hall is Rs 50,000.
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