Nhà bác An kinh doanh nhà hàng ăn. Trong vuông có một cái ao hình ABCDE (như hình vẽ bên dưới). Bác muốn đo trụ và đồ bể tông xây dựng một cái chòi ở lòng ao để phục vụ thêm đồ uống cho khách sau khi ăn

To solve this problem, we first need to understand the given information and the geometric shapes involved. The setup involves a restaurant owner, an area shaped as a square, and a circular pond represented by points ABCDE.

### Information Given:
1. The **pond** has a radius of **10 m**.
2. The horizontal distance from line AE to line BC is **40 m** and **30 m**, respectively.
3. The vertical distance from point A to the x-axis (line OA) is **40 m**, and from point B to the x-axis (line OB) is **20 m**.
4. The parabola represented by points A and B intersects at point O.

### Steps to Solve:
1. **Identify Coordinates of Points**:
- Assume point A is at (0, 40) and point B is at (40, 20).

2. **Determine the Equation of the Parabola**:
- The general form of a parabola can be given by \( y = ax^2 + bx + c \). We can use the coordinates of points A and B to find the coefficients.

3. **Calculate the Intersection**:
- Set up the equations, then calculate where the parabola intersects with the line OA and line OB.

4. **Determine the Shape of the Structure**:
- Once the equations are established, we find the dimensions of the shaded area (the area where the structure can be built).

5. **Use the Dimensions to Calculate Material Needs**:
- Once the area is determined, calculate the total material needed for construction based on the dimensions provided.

### Additional Notes:
- To find the length from **AB** to point O and the exact intersection, use algebraic methods or a graphing calculator if necessary.
- The volume of materials and costs can be determined once the dimensions involving height and area are clarified.

If you need more specific calculations or assistance with any particular part, feel free to ask!