https://file.aiquickdraw.com/mathbot/file/1727099803062v0whpp5f.jpg

To find the area of the shaded section in the diagram, we can break it down into simpler geometric shapes. The figure seems to be composed of a rectangle at the bottom and a trapezium or triangular shape on top.

### Step-by-step calculation:

1. **Bottom Rectangle (ABFG):**
   - Length \( = 12 \, \text{cm} \) (from \( A \) to \( G \)).
   - Height \( = 9 \, \text{cm} \) (from \( A \) to \( B \)).
   
   Area of rectangle = \( \text{length} \times \text{height} = 12 \times 9 = 108 \, \text{cm}^2 \).

2. **Top Trapezium or Triangle (CDEF):**
   - The base of the trapezium at the bottom is \( 12 \, \text{cm} \) (from \( C \) to \( F \)).
   - The top length is \( 6 + 6 = 12 \, \text{cm} \) (from \( C \) to \( E \)).
   - The total height of the trapezium is \( 18 \, \text{cm} \) (from \( C \) to \( D \)) minus the height of the rectangle \( 9 \, \text{cm} \), so the height of the trapezium is \( 18 - 9 = 9 \, \text{cm} \).

   For a trapezium:
   \[
   \text{Area} = \frac{1}{2} \times ( \text{Base}_1 + \text{Base}_2 ) \times \text{Height}
   \]
   Substituting the values:
   \[
   \text{Area} = \frac{1}{2} \times (12 + 12) \times 9 = \frac{1}{2} \times 24 \times 9 = 108 \, \text{cm}^2
   \]

3. **Total Area of the Shaded Section:**
   The shaded area consists of the rectangle and the trapezium on top. Adding the areas:
   \[
   \text{Total Area} = 108 \, \text{cm}^2 + 108 \, \text{cm}^2 = 216 \, \text{cm}^2
   \]

Thus, the area of the shaded section is **216 cm²**.

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Would you like further clarification on any step? Here are some related questions to explore:

1. How do you find the area of a trapezium in general cases?
2. What are other ways to divide complex shapes into simpler ones?
3. What is the difference between finding the area of a triangle and a trapezium?
4. How would the total area change if the dimensions of the rectangle were different?
5. What is the formula for the area of a complex polygon?

**Tip:** Always try breaking down complex figures into simpler, known shapes to make area calculations easier.

Find the area of the shaded section in the given diagram.

Learn how to find the area of a shaded section composed of a trapezium and a rectangle. This problem covers key geometric concepts and step-by-step calculation of area. Suitable for students in Grades 7-9.

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