To solve this, we need to determine the relationship between the area of the ceiling and the number of tiles.

1. Identify Proportion:

   • From the table, we see that when the area is $10 \, \text{sq. m}$, the number of tiles needed is $53.75$.

2. Calculate Tiles per Square Meter:

   • The number of tiles per square meter is calculated by dividing the total number of tiles by the area: $\text{Tiles per sq. m} = \frac{53.75}{10} = 5.375$

3. Formulate the Equation:

   • Let $x$ represent the area in square meters. Then, the number of tiles needed for an area $x$ can be calculated as: $\text{Number of Tiles} = 5.375 \times x$

4. General Solution:

   • For any ceiling area $x$, multiply by $5.375$ to get the number of tiles required.

Would you like further details or have additional questions?

Relative Questions:

1. How many tiles are needed for a ceiling area of 20 sq. meters?
2. If you have only 100 tiles, what is the maximum ceiling area you can cover?
3. How does changing the tile size affect the tiles per square meter calculation?
4. How would the formula change if each square meter required 6 tiles instead?
5. Can we use a similar approach to calculate other materials like paint coverage?

Tip:

Always check if there's a constant ratio in tables like these—it often leads to a straightforward solution.