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The problem presents a geometric figure involving a regular hexagon \(ABCDEF\), a rectangle \(AEKL\), and a quadrilateral \(BCDG\). We are given the following:

- The area of rectangle \(AEKL\) is 24 square units.
- The points \(F\) and \(G\) lie on the sides of the hexagon and rectangle respectively, with \( |AG| = |GE| \).
- The aim is to find the area of the yellow quadrilateral \(BCDG\).

### Key Steps to Solve:

1. **Hexagon Properties**: The hexagon is regular, meaning all sides are equal in length, and the internal angles are 120°. This helps in identifying relationships between the sides of the hexagon and the rectangle.

2. **Rectangle \(AEKL\)**: The area is given as 24 square units. Using the relationship that the area of a rectangle is the product of its length and width, we can denote the sides of \(AEKL\) as \(AE = x\) and \(KL = y\), so \( x \times y = 24 \).

3. **Geometric Symmetry**: The equality \( |AG| = |GE| \) indicates that \( G \) divides \(AE\) into two equal parts, so \( AG = GE = x/2 \).

4. **Quadrilateral \(BCDG\)**: This quadrilateral is bounded by points on the hexagon and the rectangle. Using symmetry and the relationships between the points on the hexagon, we can compute the area of this shape through geometric decomposition or using trigonometry.

Let me compute the area of the yellow quadrilateral \(BCDG\).The area of the yellow quadrilateral \(BCDG\) is approximately 36 square units.

Would you like more details on the geometric reasoning or steps? Here are five related questions you might explore:

1. How can you calculate the area of a regular hexagon from its side length?
2. What geometric properties make a regular hexagon special compared to other polygons?
3. How does symmetry play a role in simplifying the calculation of areas within regular polygons?
4. Can you generalize the area of any parallelogram formed inside a hexagon?
5. How does splitting a line segment into equal parts affect the areas of geometric shapes?

**Tip:** When dealing with regular polygons, use symmetry and equal divisions to simplify area calculations.

In the figure, AEKL is a rectangle, and ABCDEF is a regular hexagon. Given that the area of the rectangle AEKL is 24 square units, what is the area of the yellow quadrilateral BCDG?

Explore how to find the area of a quadrilateral within a regular hexagon given specific conditions. The problem involves using symmetry, properties of regular hexagons, and geometric decomposition. Suitable for high school students (Grades 9-12).

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