Basic Volume/Cost Optimization Question

I've been using a review book to prepare for a calc 2 course over the summer, and I legitimately think the book has made a slight error in its answer.

Trying to find optimal cost for an open top 20 m³ cube with a length twice its width. Costs are given for the base material and side material, with the goal being to find the lowest possible. The book and I have the same calculation in terms of calculating the dimensions (20=2x²y, so height is y=10/x² for a base measuring width=x, length=2x.) The only disconnect is that the book says that the sides each have a surface area of xy, despite having established the base is not a square with equal lengths. Wouldn't the side surface area calculation be 2(xy)+2(2xy), to account for half the sides being twice the length of the other?