An open-top rectangular box is \(12~\text{in}\). by \(8~\text{in}\). by \(5~\text{in}\). Determine the outside surfaces that are painted and excluded, and write the area setup.

Build the setup from the surfaces that exist and are painted, rather than automatically using a closed-prism formula. The open box contributes one bottom, two long side faces, and two short side faces, while the absent top contributes nothing. Write one area term for the bottom and doubled terms for each side-face pair, leaving the requested setup unsimplified.