Trevor has built a bookshelf which has dimensions of 2 feet by 2 feet for each shelf and a height of 4 feet with a solid board across the back. He wants to paint all surfaces, including the undersides of each shelf and both sides of the backboard.
To calculate the total paintable area, we need to find the area of each shelf and the backboard, and then add them together.
Each shelf has an area of 2 feet x 2 feet = 4 square feet. There are a total of 4 shelves, so the total area of all the shelves is 4 shelves x 4 square feet per shelf = 16 square feet.
The backboard has a height of 4 feet and a width of 2 feet, so its area is 4 feet x 2 feet = 8 square feet. Since both sides of the backboard need to be painted, the total area of the backboard is 2 x 8 square feet = 16 square feet.
Therefore, the total paintable area of the bookshelf is the sum of the area of all the shelves and the backboard, which is:
16 square feet (area of shelves) + 16 square feet (area of backboard) = 32 square feet
Therefore, Trevor will need to paint a total of 32 square feet of surface area on the bookshelf.