The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per `m^2` is Rs. 4.

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the area of one rhombus tile.
The area \( A \) of a rhombus can be calculated using the formula:
\[ A = \frac{1}{2} \times d_1 \times d_2 \]
where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

Given:
- \( d_1 = 45 \, \text{cm} \)
- \( d_2 = 30 \, \text{cm} \)

Substituting the values:
\[ A = \frac{1}{2} \times 45 \times 30 \]
\[ A = \frac{1}{2} \times 1350 = 675 \, \text{cm}^2 \]

### Step 2: Calculate the total area of 3000 tiles.
To find the total area of 3000 tiles, we multiply the area of one tile by the number of tiles:
\[ \text{Total Area} = 3000 \times 675 \, \text{cm}^2 \]
\[ \text{Total Area} = 2025000 \, \text{cm}^2 \]

### Step 3: Convert the total area from cm² to m².
To convert from cm² to m², we divide by 10,000 (since \( 1 \, \text{m}^2 = 10,000 \, \text{cm}^2 \)):
\[ \text{Total Area in m}^2 = \frac{2025000}{10000} = 202.5 \, \text{m}^2 \]

### Step 4: Calculate the total cost of polishing the floor.
The cost of polishing per m² is Rs. 4. Therefore, the total cost can be calculated as:
\[ \text{Total Cost} = \text{Total Area in m}^2 \times \text{Cost per m}^2 \]
\[ \text{Total Cost} = 202.5 \times 4 = 810 \, \text{Rs.} \]

### Final Answer:
The total cost of polishing the floor is **Rs. 810**.

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