Sure! Let's tackle this problem step-by-step:
Step 1: Understand the tile and margin dimensions
Each rectangular tile measures 15 cm by 18 cm. There's a uniform margin of 5 cm around the entire floor where tiles are not placed.
Step 2: Determine the dimensions of the area covered by the tiles
Since the tiles are rectangular and the floor is square, for simplicity, let's assume the tiles are arranged such that their combined dimensions (length and width) form the side of a smaller square within the larger floor square.
- Tile length = 15 cm
- Tile width = 18 cm
Adding these dimensions together, we get:
Required side length of the area covered by the tiles = 15 cm + 18 cm = 33 cm
Step 3: Determining the side length of the entire floor
The margin around the tiles adds to the dimension on each side of the floor, effectively increasing the total side length of the square floor.
- Margin width on one side = 5 cm
- Since there is margin on all sides, we have to double the margin width for each side for a uniform margin around.
Total side length of the floor = Side length of the area covered by tiles + 2 Margin width
= 33 cm + 2 5 cm
= 33 cm + 10 cm
= 43 cm
Step 4: Calculate the area of the entire square floor
The area of a square is given by the side length squared.
Therefore, the area of the entire square floor is:
[tex]\[ \text{Floor Area} = \text{Side Length}^2 = 43 \text{ cm} \times 43 \text{ cm} = 1849 \text{ cm}^2 \][/tex]
So, the minimum area of the floor required to accommodate the tiles, leaving a uniform margin of 5 cm all around, is [tex]\( 1849 \, \text{cm}^2 \)[/tex].
