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The task here involves calculating lengths and areas in the provided triangle diagram. Here’s a step-by-step outline of what needs to be calculated:

### Given Information:
- **AB** = 14
- **∠CAB** = 60°
- **CE = 5** and **ED = 7** (indicating segments along **AB**)
- The height from **A** to line **CD** is given as **18**, which could be useful in calculating areas.

### Questions to Answer:
1. **Calculate Lengths of Segments**:
   - \( \overline{EF} \)
   - \( \overline{FD} \)
   - \( \overline{DB} \)

2. **Calculate Areas**:
   - Area of quadrilateral **ABCD**
   - Area of triangle **EFG**

Would you like to confirm any of the information above, or should I proceed with the calculations? 

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Here are some questions to deepen understanding:

1. What formula is used to calculate the area of a triangle with a given angle and two sides?
2. How does breaking a line into segments help in finding unknown lengths?
3. What is the relationship between similar triangles and their side lengths?
4. How is the area of a quadrilateral calculated when the shape is not a simple rectangle?
5. How does knowing the height of a triangle assist in calculating its area?

**Tip**: When dealing with triangles, always check if they can be divided into smaller, similar triangles, which simplifies many calculations.

Calculate the lengths of segments EF, FD, and DB, and the areas of quadrilateral ABCD and triangle EFG based on the provided triangle diagram, where AB = 14, ∠CAB = 60°, CE = 5, ED = 7, and the height from A to line CD is 18.

Learn how to calculate the lengths of segments EF, FD, and DB, and the areas of quadrilateral ABCD and triangle EFG in a complex geometric diagram. This problem covers geometry, trigonometry, and area calculation techniques, suitable for high school students.

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