A rectangular banquet hall measuring 25.2 m in length and 16.8 m in width is to be paved entirely with identical square marble tiles, each having a perimeter of 240 cm (with a side length of 60 cm). Calculate the total number of tiles required to cover the floor surface completely.

The correct option is 1176.

To find the total number of square marble tiles required to pave the banquet hall, we need to calculate the total area of the floor and divide it by the area of a single square tile.

Step 1: Convert the hall dimensions from meters to centimeters.

Length of the hall = 25.2 m = 25.2 × 100 cm = 2520 cm

Width of the hall = 16.8 m = 16.8 × 100 cm = 1680 cm

Step 2: Calculate the total floor area of the banquet hall.

$\text{Area of hall}=\text{Length}\times \text{Width}$

$\text{Area of hall}=2520\text{cm}\times 1680\text{cm}=4233600{\text{cm}}^2$

Step 3: Calculate the area of a single square marble tile.

Each square tile has a side length of 60 cm (which corresponds to a perimeter of 4 × 60 cm = 240 cm).

$\text{Area of one tile}=\text{Side}\times \text{Side}$

$\text{Area of one tile}=60\text{cm}\times 60\text{cm}=3600{\text{cm}}^2$

Step 4: Calculate the total number of tiles required.

$\text{Total tiles}=\frac{\text{Area of hall}}{\text{Area of one tile}}$

$\text{Total tiles}=\frac{4233600}{3600}=1176$

Alternative Method (Tile grid count):

$\text{Number of tiles along the length}=\frac{2520}{60}=42$

$\text{Number of tiles along the width}=\frac{1680}{60}=28$

$\text{Total tiles}=42\times 28=1176$

Thus, the total number of tiles required to cover the floor surface completely is 1176.