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To find the shaded area of the shape, let's break down the shape into manageable components:

### Step 1: Calculate the area of the entire rectangle.
- Dimensions of the rectangle: 11 m (width) × 9.9 m (height).
- Area of the rectangle = \( 11 \times 9.9 = 108.9 \text{ m}^2 \).

### Step 2: Calculate the area of the triangular cutout.
- The base of the triangle is 8.5 m, and the height is the difference between the total height of the rectangle (9.9 m) and the height from the base to the triangle's top (5.4 m).
- Height of the triangle = \( 9.9 - 5.4 = 4.5 \text{ m} \).

- Area of the triangle = \( \frac{1}{2} \times 8.5 \times 4.5 = 19.125 \text{ m}^2 \).

### Step 3: Subtract the area of the triangle from the area of the rectangle.
- Shaded area = \( 108.9 - 19.125 = 89.775 \text{ m}^2 \).

The shaded area is \( 89.775 \text{ m}^2 \).

Would you like more details or have any questions?

Here are some related questions:
1. How would the area calculation change if the triangular cutout had a different height?
2. Can we calculate the perimeter of the shaded area?
3. How can we calculate the centroid of the shaded shape?
4. What would happen if the triangle was not isosceles?
5. How do different shapes influence the complexity of area calculations?

**Tip:** When working with complex shapes, break them down into simple geometric figures like rectangles, triangles, or circles for easier calculations.

Find the shaded area of the given geometric shape with dimensions: 11 m × 9.9 m for the outer rectangle, 8.5 m base, and 5.4 m height for the triangular cutout.

Learn how to calculate the shaded area of a complex shape. This problem involves subtracting the area of a triangle (8.5 m base, 4.5 m height) from a rectangle (11 m × 9.9 m), resulting in a total shaded area of 89.775 square meters. Suitable for students in Grades 6-8.

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