Squares change in area

[Dillinger4]

If a square has a side of s in. and the side is increased by 4.5 in. express the change in area in terms of s

If the perimeter of a square is represented as a = 2l + 2w and we are only increasing one side then we should have a = 2(4.5) + 2w. My book seems to give the answer 9s + 20.25 Where does the 20.25 come from. If we are only increasing one side and they fail to tell us which side is being increased then either the length or the with is increased but not bolth.

Also, since they are saying that a square has a side of s inches and is increased by 4.5 inches are we supposed to assume that the square started out with a side of 0 inches? but then it wouldnt be a square. Shouldnt the equation be a = 2(s + 4.5) + 2w

[twanvl]

You are talking about the permimiter, while the exercise asks about the area. And the side of a square menas the length of all sides, otherwise it wouldn't be a square.
A = s²
A' = s'² = (s+4.5)²
Since (a+b)²=a² + 2ab + b²
A' = s² + 2*4.5s + 4.5²

[Dillinger4]

Ah ok. That's why i was getting confused. Area not perimeter.