To find the area of the composite figure, we need to calculate the areas of its individual components (the parallelogram, square, and rectangle) and add them together.

Step 1: Break down the figure

The figure consists of:

1. A parallelogram on top.
2. A square in the middle (3.5 in × 3.5 in).
3. A rectangle at the bottom.

Step 2: Calculate areas

(a) Area of the parallelogram

The formula for the area of a parallelogram is: $\text{Area} = \text{base} \times \text{height}$ Here, the base is 10 inches, and the height is 3.5 inches: $\text{Area}_{\text{parallelogram}} = 10 \times 3.5 = 35 \, \text{in}^2$

(b) Area of the square

The formula for the area of a square is: $\text{Area} = \text{side}^2$ The side of the square is 3.5 inches: $\text{Area}_{\text{square}} = 3.5 \times 3.5 = 12.25 \, \text{in}^2$

(c) Area of the rectangle

The formula for the area of a rectangle is: $\text{Area} = \text{length} \times \text{width}$ Here, the length is 12.5 inches, and the width is 6 inches: $\text{Area}_{\text{rectangle}} = 12.5 \times 6 = 75 \, \text{in}^2$

Step 3: Add the areas

The total area is: $\text{Total Area} = \text{Area}_{\text{parallelogram}} + \text{Area}_{\text{square}} + \text{Area}_{\text{rectangle}}$ Substitute the values: $\text{Total Area} = 35 + 12.25 + 75 = 122.25 \, \text{in}^2$

Final Answer:

The total area of the figure is 122.25 square inches.

Would you like a more detailed explanation of any step or clarification?

Here are 5 related questions to expand your understanding:

1. How does the formula for the area of a parallelogram differ from a rectangle?
2. Can you calculate the perimeter of this composite figure?
3. How would the area change if the parallelogram’s height were doubled?
4. What is the difference between composite figures and simple figures in geometry?
5. Can you find the area of a triangle that fits inside this figure?

Tip: For composite shapes, always break them into simpler components like rectangles, triangles, or circles.