https://file.aiquickdraw.com/mathbot/file/1727214973726hcwl4oo6.jpg

To find the area of the given irregular quadrilateral, we can divide the shape into two right triangles and one rectangle.

### Step 1: Identify components
- There is a rectangle at the bottom with dimensions:
  - Base = 10 m
  - Height = 8 m
- Above the rectangle, there are two right triangles on each side, with one triangle's height being 8 m and the other being 9 m. The slanted side has a total length of 11 m, and the horizontal base between the two triangles is 10 m.

### Step 2: Calculate the area of the rectangle
The area of a rectangle is:
\[
A_{\text{rectangle}} = \text{base} \times \text{height} = 10 \times 8 = 80 \text{ m}^2
\]

### Step 3: Find the missing part
To find the area of the triangular portion above the rectangle, we can consider it as the area of a trapezoid. The area of a trapezoid is given by:
\[
A_{\text{trapezoid}} = \frac{1}{2} \times (b_1 + b_2) \times h
\]
Where:
- \(b_1 = 10 \text{ m}\) (base of the rectangle),
- \(b_2 = 11 \text{ m}\) (slanted top side),
- \(h = \) height difference = 9 m - 8 m = 1 m.

\[
A_{\text{trapezoid}} = \frac{1}{2} \times (10 + 11) \times 1 = \frac{1}{2} \times 21 \times 1 = 10.5 \text{ m}^2
\]

### Step 4: Total area
Now, we sum the areas of the rectangle and the trapezoid:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{trapezoid}} = 80 + 10.5 = 90.5 \text{ m}^2
\]

### Final Answer:
The total area of the figure is **90.5 m²**.

Would you like more details on any step or have any other questions?

#### Related Questions:
1. How do you calculate the perimeter of this shape?
2. What is the height of the trapezoid portion from the top slant to the rectangle?
3. Can you explain how to calculate the area of a right triangle?
4. How do trapezoids differ from triangles in terms of area calculation?
5. How can you find the total surface area of a 3D shape based on this figure?

#### Tip:
When dealing with irregular shapes, breaking them into simpler parts (like rectangles, triangles, or trapezoids) makes area calculation easier.

Find the area of the given irregular quadrilateral.

Learn how to calculate the area of an irregular quadrilateral by breaking it into a rectangle and a trapezoid. Includes step-by-step instructions using the area formulas for both shapes. Suitable for students in Grades 7-9.

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