Step 1: Convert Measurements to Centimeters
- Height of the room: 3 meters = 300 cm
- Length of each side of the room: 1.5 meters = 150 cm
Step 2: Calculate the Area of the Floor
The floor is a square with each side measuring 150 cm.
\text{Area of the floor} = 150 \text{cm} \times 150 \text{cm} = 22,500 \text{cm}^2
Step 3: Calculate the Area of the Walls
Each wall is a rectangle with a height of 300 cm and a width of 150 cm. There are 4 walls.
\text{Area of one wall} = 300 \text{cm} \times 150 \text{cm} = 45,000 \text{cm}^2
\text{Total area of the walls} = 4 \times 45,000 \text{cm}^2 = 180,000 \text{cm}^2
Step 4: Calculate the Total Area to be Tiled
Add the area of the floor and the area of the walls.
\text{Total area to be tiled} = 22,500 \text{cm}^2 + 180,000 \text{cm}^2 = 202,500 \text{cm}^2
Step 5: Calculate the Area of One Tile
Each tile is 30 cm x 30 cm.
\text{Area of one tile} = 30 \text{cm} \times 30 \text{cm} = 900 \text{cm}^2
Step 6: Calculate the Number of Tiles Needed
Divide the total area to be tiled by the area of one tile.
\text{Number of tiles} = \frac{202,500 \text{cm}^2}{900 \text{cm}^2} = 225
Therefore, 225 tiles are needed to tile the entire room, including the floor and all four walls.
225