When estimating the area of a land, it usually helps when approximating the land to a shape.
The shape of the United States can be approximated to a semi - circle.
For estimating the area of this semi circle, it helps to estimate the diameter. This can be estimated in multiple ways, for example – estimating the distance between two corner cities of the United States such as San Francisco to New York City. Or the distance between two railway lines between cities.
Let us choose the distance between two corner cities. The distance between New York City and San Francisco is about 4680 km. Thus, the radius can be 2340 km.
Or, the area of the United States can be π * r^2 * ½
Or, 3.14 * 2340 * 2340 * ½ = 85,96,692
Or, 8.596692 × 10^6 sq. km
Or, 3.319201338 × 10^6 sq. miles
Or, about 3.3 million square miles.
This is a good approximate because the actual area of the United States in about 3.8 million square miles.