The question asks about the area of a square room. In the image, we see a rectangular section of the floor being tiled. The tile covers an area of 18 square feet, and the dimensions of the tiled section are 12 ft by 15 ft.

To find the area of the room, we know that the room is square. The dimensions of a square room are equal, so both sides of the room will be the same length. To calculate the area of the square room, we will use the formula for the area of a square:

$\text{Area of the room} = \text{side}^2$

Since we don't have the exact side length of the room, we can calculate it using the given dimensions of the rectangular section tiled. The room's side length must be at least as large as the larger of the two given dimensions (12 ft or 15 ft).

Thus, the side of the room is 15 feet, so the area is:

$\text{Area of the room} = 15^2 = 225 \text{ square feet}$

Therefore, the area of the room is 225 square feet.

Would you like to go over any details or have other questions on this problem? Here's some additional content for your understanding:

1. How do we calculate the area of a square room when given side lengths?
2. What is the difference between calculating the area of a rectangle and a square?
3. How do you convert square feet into other units like square inches or square yards?
4. What other ways can we approach problems with given tile dimensions and room area?
5. How do dimensions of objects affect the total area calculation in real-world applications?

Tip: Always remember that for squares, all sides are equal, making area calculations simpler!