Yes, it is often possible to figure out the size of distant objects, as long as they aren’t too small. The key is in knowing the distance to the object. For example, if someone holds a nickel at arm’s length and then has someone hold the nickel 200 yards away, the coin may appear to be smaller, but its size really hasn’t changed. If a person knows how large an object appears to be, and how distant it is, they can work backward to determine the true size of the object. Simply put, this is also how astronomers work out the size of distant objects in outer space.
Using parallax to determine the distance to a star is done by calculating the apparent shift of a star as the Earth orbits the Sun.