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To find the area of hexagon \( ABCDEF \), let's break it into manageable parts.

The hexagon is composed of a rectangle and two right triangles, one on each side of the rectangle.

### Key Information:
- \( AB = FE = 14 \, \text{cm} \)
- \( AF = 20 \, \text{cm} \)
- \( CD = 16 \, \text{cm} \)
- \( BE = 24 \, \text{cm} \)
- \( CD \parallel AF \)

The shape seems to be composed of:
1. A rectangle \( ABFE \) with width \( AF = 20 \, \text{cm} \) and height \( AB = 14 \, \text{cm} \).
2. Two right triangles on the sides.

We can break this into two parts:

1. **Area of the rectangle \( ABFE \):**
   \[
   \text{Area of rectangle} = \text{width} \times \text{height} = 20 \times 14 = 280 \, \text{cm}^2
   \]

2. **Area of the trapezium \( CDEF \):**
   The height of the trapezium is \( BE = 24 \, \text{cm} \), the parallel sides are \( CD = 16 \, \text{cm} \) and \( AF = 20 \, \text{cm} \). The area of a trapezium is calculated using:
   \[
   \text{Area of trapezium} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}
   \]
   Substituting the values:
   \[
   \text{Area of trapezium} = \frac{1}{2} \times (16 + 20) \times 24 = \frac{1}{2} \times 36 \times 24 = 432 \, \text{cm}^2
   \]

### Total Area:
The total area of the hexagon is the sum of the areas of the rectangle and trapezium:
\[
\text{Total area} = 280 \, \text{cm}^2 + 432 \, \text{cm}^2 = 712 \, \text{cm}^2
\]

Thus, the area of hexagon \( ABCDEF \) is \( 712 \, \text{cm}^2 \).

Would you like further details or explanations on any step?

Here are 5 related questions you might find useful:
1. How is the formula for the area of a trapezium derived?
2. What are the properties of hexagons that simplify area calculation?
3. How can we find the area of a polygon using triangulation?
4. What role does symmetry play in breaking complex shapes into simpler ones?
5. Can we calculate the area of irregular polygons using coordinate geometry?

**Tip:** When solving geometric problems, breaking complex figures into simpler shapes like triangles and rectangles helps simplify area calculations.

Work out the area of hexagon ABCDEF. Given: AB = 14 cm, FE = 14 cm, AF = 20 cm, CD = 16 cm, BE = 24 cm, and CD is parallel to AF.

Learn how to calculate the area of hexagon ABCDEF using a step-by-step breakdown of the trapezium and rectangle parts. This problem involves geometry concepts such as parallel lines, trapeziums, and rectangles, making it ideal for students in Grades 9-10.

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