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To find the area of the given figure, which appears to be a composite shape consisting of a trapezoid with a triangle on top, we can break it down into these two simpler shapes, calculate the area of each, and then sum the areas.

### Step-by-Step Solution:

1. **Identify the Shapes and Dimensions:**
   - The **trapezoid** has:
     - Bases: \(4.5' + 4.5' = 9'\) (top base) and \(2' + 2' = 12'\) (bottom base)
     - Height: \(8'\)
   - The **triangle** on top has:
     - Base: \(9'\)
     - Height: \(4'\)

2. **Calculate the Area of the Trapezoid:**
   - The formula for the area of a trapezoid is:
     \[
     \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
     \]
   - Plugging in the values:
     \[
     \text{Area of Trapezoid} = \frac{1}{2} \times (9' + 12') \times 8' = \frac{1}{2} \times 21' \times 8' = \frac{168}{2} = 84 \text{ square feet}
     \]

3. **Calculate the Area of the Triangle:**
   - The formula for the area of a triangle is:
     \[
     \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
     \]
   - Plugging in the values:
     \[
     \text{Area of Triangle} = \frac{1}{2} \times 9' \times 4' = \frac{36}{2} = 18 \text{ square feet}
     \]

4. **Sum the Areas:**
   \[
   \text{Total Area} = 84 \text{ square feet} + 18 \text{ square feet} = 102 \text{ square feet}
   \]

Thus, the area of the entire figure is **102 square feet**.

Would you like further explanation or do you have other questions?

### Related Questions:
1. How do you calculate the perimeter of a composite shape like this?
2. What are the properties of a trapezoid?
3. How can you find the area of irregular polygons?
4. How would the area change if the triangle were isosceles?
5. What is the difference between calculating the area of a trapezoid and a parallelogram?
6. How do you use Heron's formula for finding the area of a triangle with different side lengths?
7. How do changes in the dimensions of one part of a composite shape affect the overall area?
8. How do you calculate the centroid of this composite shape?

**Tip:** When working with composite shapes, always ensure you correctly identify all component shapes, as missing or misinterpreting a part can lead to errors in the final area calculation.

Learn how to find the area of a composite shape consisting of a trapezoid with a triangle on top. Step-by-step solution provided, including formulas for calculating the area of both shapes and their sum. Suitable for students in Grades 6-8.

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