To find the area of the given irregular figure, we can break it down into two rectangles, then calculate the area of each and add them together.

Step-by-Step Solution:

1. Identify the Two Rectangles:

   • Rectangle 1: The bottom part with dimensions 10 inches by 28 inches.
   • Rectangle 2: The upper part with dimensions 8 inches by 30 inches.

2. Calculate the Area of Each Rectangle:

   • Rectangle 1 Area = $\text{Length} \times \text{Width} = 10 \, \text{in} \times 28 \, \text{in} = 280 \, \text{square inches}$.
   • Rectangle 2 Area = $\text{Length} \times \text{Width} = 8 \, \text{in} \times 30 \, \text{in} = 240 \, \text{square inches}$.

3. Add the Areas Together:

   • Total Area = $280 \, \text{square inches} + 240 \, \text{square inches} = 520 \, \text{square inches}$.

Answer:

The area of the irregular figure is 520 square inches.

Would you like more details or have any questions about the steps?

Here are five related questions that might expand your understanding:

1. How would the area change if the dimensions of the rectangles were increased by 10%?
2. What other methods could be used to find the area of irregular shapes?
3. How can you determine the perimeter of this figure?
4. What is the significance of breaking down complex shapes into basic geometric figures for calculations?
5. How can we calculate the area of a figure with curved edges?

Tip: When working with irregular figures, try dividing them into simpler shapes like rectangles or triangles, as it often makes area calculations much easier.