To calculate the surface area of the pool covered by tiles, we need to determine the total area of the four sides (the walls) and the bottom of the pool. The pool has:
- Length = 25 feet
- Width = 12 feet
- Depth = 4.5 feet
Step 1: Calculate the area of the bottom of the pool (base).
The area of the bottom (base) is calculated as: \[ \text{Area}_{\text{bottom}} = \text{Length} \times \text{Width} = 25 , \text{ft} \times 12 , \text{ft} = 300 , \text{ft}^2 \]
Step 2: Calculate the area of the sides of the pool.
The pool has two lengths of height and two widths of height.
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Area of the two longer sides (length): \[ \text{Area}_{\text{long sides}} = 2 \times (\text{Length} \times \text{Depth}) = 2 \times (25 , \text{ft} \times 4.5 , \text{ft}) = 2 \times 112.5 , \text{ft}^2 = 225 , \text{ft}^2 \]
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Area of the two shorter sides (width): \[ \text{Area}_{\text{short sides}} = 2 \times (\text{Width} \times \text{Depth}) = 2 \times (12 , \text{ft} \times 4.5 , \text{ft}) = 2 \times 54 , \text{ft}^2 = 108 , \text{ft}^2 \]
Step 3: Calculate the total area of the sides.
\[ \text{Total Area}{\text{sides}} = \text{Area}{\text{long sides}} + \text{Area}_{\text{short sides}} = 225 , \text{ft}^2 + 108 , \text{ft}^2 = 333 , \text{ft}^2 \]
Step 4: Total surface area of the pool covered by tiles.
Now we add the area of the bottom and the sides together: \[ \text{Total Surface Area} = \text{Area}{\text{bottom}} + \text{Total Area}{\text{sides}} = 300 , \text{ft}^2 + 333 , \text{ft}^2 = 633 , \text{ft}^2 \]
Therefore, the total surface area of the pool covered by tiles is:
633 ft² (or 633 ft squared)
Final Answer: 633 ft².