A house has a front yard with an area of 4,200 ft.2

Let \( A \) represent the area of the house in square feet. The area of the front yard is given as 4,200 ft².

According to the information provided, the total area of the house plus the area of the yard can be expressed as:
\[
A + 4200
\]
It is also stated that the total area (house + yard) is 8 times the area of the house alone. This can be represented by the equation:
\[
A + 4200 = 8A
\]

This equation models the given real-world situation.