How many tiles 20 cm by 40 cm will be required to pave the floor of a prayer hall of a room 16 m long and 9 m wide :

Options

A. 18000
B. 2700
C. 1800
D. 14400

Answer

To solve the problem of how many tiles of dimensions 20 cm by 40 cm are required to pave the floor of a prayer hall measuring 16 m by 9 m, we will follow these steps:

### Step 1: Convert the dimensions of the tiles from centimeters to meters.
- The length of the tile is 20 cm, which is equal to \( \frac{20}{100} = 0.2 \) m.
- The width of the tile is 40 cm, which is equal to \( \frac{40}{100} = 0.4 \) m.

### Step 2: Calculate the area of the floor.
- The area of the floor can be calculated using the formula:
\[ \text{Area of the floor} = \text{Length} \times \text{Width} \]
- For the prayer hall:
\[ \text{Area of the floor} = 16 \, \text{m} \times 9 \, \text{m} = 144 \, \text{m}^2 \]

### Step 3: Calculate the area of one tile.
- The area of one tile is calculated as follows:
\[ \text{Area of one tile} = \text{Length} \times \text{Width} \]
- For one tile:
\[ \text{Area of one tile} = 0.2 \, \text{m} \times 0.4 \, \text{m} = 0.08 \, \text{m}^2 \]

### Step 4: Calculate the number of tiles required.
- To find the number of tiles required, divide the area of the floor by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area of the floor}}{\text{Area of one tile}} = \frac{144 \, \text{m}^2}{0.08 \, \text{m}^2} \]
- Performing the calculation:
\[ \text{Number of tiles} = 1800 \]

### Conclusion:
Thus, the total number of tiles required to pave the floor of the prayer hall is **1800 tiles**.

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