https://file.aiquickdraw.com/mathbot/file/1723167856293h6d934yv.jpg

To find the area of the entire figure, we'll break it down into simpler shapes whose areas can be calculated easily. The figure consists of a rectangle and two trapezoids (one above and one below the rectangle).

### Step 1: Analyze the shapes
1. **Rectangle**: 
   - Width = 4 feet
   - Height = 8 feet

2. **Upper trapezoid**:
   - The two parallel sides are 4 feet (bottom of the trapezoid) and 4 + 2 + 2 = 8 feet (top of the trapezoid).
   - The height of the trapezoid = 4.5 feet.

3. **Lower trapezoid**:
   - The two parallel sides are 4 feet (bottom of the rectangle) and 8 feet (bottom of the trapezoid).
   - The height of the trapezoid = 4.5 feet.

### Step 2: Calculate the area of each shape

1. **Area of the Rectangle**:
   \[
   \text{Area} = \text{Width} \times \text{Height} = 4 \times 8 = 32 \text{ square feet}
   \]

2. **Area of the Upper Trapezoid**:
   \[
   \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
   \]
   Substituting the values:
   \[
   \text{Area} = \frac{1}{2} \times (4 + 8) \times 4.5 = \frac{1}{2} \times 12 \times 4.5 = 6 \times 4.5 = 27 \text{ square feet}
   \]

3. **Area of the Lower Trapezoid**:
   \[
   \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
   \]
   Substituting the values:
   \[
   \text{Area} = \frac{1}{2} \times (4 + 8) \times 4.5 = 27 \text{ square feet}
   \]

### Step 3: Add the areas to get the total area
\[
\text{Total Area} = \text{Area of Rectangle} + \text{Area of Upper Trapezoid} + \text{Area of Lower Trapezoid}
\]
\[
\text{Total Area} = 32 + 27 + 27 = 86 \text{ square feet}
\]

So, the area of the entire figure is **86 square feet**.

Would you like more details or have any questions?

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Here are 8 related questions for further exploration:

1. What is the area of the figure if the height of the rectangle were doubled?
2. How would the total area change if the trapezoids had different heights?
3. What would be the total area if the width of the rectangle were increased by 50%?
4. How would you calculate the area if the trapezoid bases were not parallel?
5. Can you find the perimeter of this figure using the given dimensions?
6. How does changing the dimensions of the trapezoid bases affect the overall area?
7. How would the total area change if the height of the rectangle were reduced by half?
8. What if the height of the trapezoids were different? How would that affect the area?

**Tip:** When solving complex geometry problems, breaking down the figure into simpler shapes makes the calculations easier.

Learn how to calculate the area of a complex figure composed of a rectangle and two trapezoids. Step-by-step guide with detailed formulas and calculations. Suitable for high school students and geometry enthusiasts.

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