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The swimming pool in the image is a trapezoidal prism, with different wall heights (2 m on one end, and 1.2 m on the other), a width of 16 m, and a length of 50 m. To solve the problem, let's calculate the area of the surfaces that need to be tiled, which include the base and the four walls.

### Part a: Total Area of Tiles
1. **Base Area** (rectangular):
   - Length = 50 m
   - Width = 16 m
   \[
   \text{Base Area} = 50 \times 16 = 800 \, \text{m}^2
   \]

2. **Side Walls Areas**:
   - **Front and Back Walls (Trapezoidal)**:
     The height of the front and back walls is trapezoidal, with one side being 2 m and the other side being 1.2 m.
     - Trapezoid area formula: \(\text{Area} = \frac{1}{2} \times (a + b) \times h\)
     - Height (h) = 16 m, \(a = 2 \, \text{m}\), and \(b = 1.2 \, \text{m}\):
     \[
     \text{Area of each trapezoidal wall} = \frac{1}{2} \times (2 + 1.2) \times 16 = 25.6 \, \text{m}^2
     \]
     Since there are two such walls (front and back):
     \[
     \text{Total trapezoidal walls area} = 2 \times 25.6 = 51.2 \, \text{m}^2
     \]

   - **Side Walls (Rectangular)**:
     - One side wall has a height of 2 m, and the other has a height of 1.2 m, both with a length of 50 m.
     \[
     \text{Area of taller wall} = 50 \times 2 = 100 \, \text{m}^2
     \]
     \[
     \text{Area of shorter wall} = 50 \times 1.2 = 60 \, \text{m}^2
     \]
     \[
     \text{Total side walls area} = 100 + 60 = 160 \, \text{m}^2
     \]

3. **Total Area of Tiles**:
   Now, summing up all the areas:
   \[
   \text{Total area} = 800 \, \text{(base)} + 51.2 \, \text{(trapezoidal walls)} + 160 \, \text{(side walls)} = 1011.2 \, \text{m}^2
   \]

### Part b: Value of the Tiles
The cost of the tiles is €25 per square meter, so:
\[
\text{Total cost} = 1011.2 \, \text{m}^2 \times 25 \, \frac{\text{€}}{\text{m}^2} = 25,280 \, \text{€}
\]

### Final Answers:
- **Total area of tiles**: 1011.2 m²
- **Total cost**: €25,280

Would you like any more details or further clarifications?

### Related Questions:
1. How do you calculate the area of irregular shapes?
2. What would be the cost if the price per square meter of tiles increased by 10%?
3. How does the trapezoid area formula relate to finding the area of other polygons?
4. What is the formula for calculating the area of a pool with different shapes?
5. How do the dimensions of the pool affect the total cost of tiling?

### Tip:
Always double-check units and dimensions when calculating areas, especially with mixed shapes like trapezoids and rectangles.

The base and walls of the swimming pool are tiled. The tiles cost €25 per m². Find the total area of the tiles and the value of the tiles.

Solve for the total area of tiles and the cost to tile a trapezoidal swimming pool. Includes step-by-step calculations using area formulas for rectangles and trapezoids. Suitable for high school geometry students.

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