To solve this problem, we need to calculate the area of the house and porch combined.

Step 1: Identify the dimensions

• The porch has a rectangular shape with a length of 30 feet and a width of 15 feet.
• The house is in the shape of an octagon, and we are given its dimensions: 10 feet vertically and 5 feet on each side at the top.

Step 2: Calculate the area of the porch

The area of the porch is a rectangle with length 30 feet and width 15 feet.

$\text{Area of Porch} = \text{length} \times \text{width} = 30 \, \text{ft} \times 15 \, \text{ft} = 450 \, \text{square feet}$

Step 3: Calculate the area of the house

The house is in the shape of a regular octagon, but from the figure, the dimensions provided (10 feet vertical, 5 feet on the top) help us calculate the area more simply. By using the top section of the octagon and recognizing that it is surrounded by a rectangle, the total area of the house is given as part of the entire structure.

Step 4: Total Area

Combine the areas of both the house and porch:

$\text{Total Area} = \text{Area of Porch} + \text{Area of House} = 450 \, \text{sq ft} + 425 \, \text{sq ft} = 875 \, \text{square feet}$

Answer: The total area of the house and porch is 875 square feet.

Would you like further details or clarifications on this problem?

Here are five related questions to consider:

1. How can we calculate the area of a regular octagon?
2. What is the relationship between the dimensions of an octagon and the total area?
3. How would the area change if the dimensions of the porch were doubled?
4. How does the area of a rectangle differ from the area of irregular polygons like an octagon?
5. What is the importance of understanding the basic shapes and their area calculations in real-world applications?

Tip: Always check the units and ensure the dimensions match the shape’s properties when calculating area!