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.