Short Answer 
To determine the total painted area for the wooden box, first gather the dimensions (1 ft height, 3 ft width, 5 ft length). The total surface area, considering the top and four sides but excluding the bottom, is 31 square feet, calculated from the areas of the sides (10 sq ft and 6 sq ft) and the top (15 sq ft).
Step 1: Gather Box Dimensions
To calculate the total area that Bob needs to paint, start by noting the dimensions of the wooden box which are essential for determining the surface areas. The dimensions are:
- Height: 1 foot
- Width: 3 feet
- Length: 5 feet
Remember that the bottom will not be painted as it rests on the floor, focusing solely on the top and four sides.
Step 2: Calculate Surface Areas of Sides
Next, compute the areas of the four sides of the box. This involves breaking it down into two pairs of rectangles:
- For the two longer sides, each measuring 1 foot high by 5 feet long, the total area is calculated as: 2 x (1 x 5) = 10 square feet.
- For the two shorter sides, each measuring 1 foot high by 3 feet wide, the total area is: 2 x (1 x 3) = 6 square feet.
Step 3: Calculate the Area of the Top and Total Painted Area
The last step is to find the area of the top of the box, which measures 3 feet by 5 feet, leading to a total area of: 3 x 5 = 15 square feet. Now, add together the areas of the sides and the top:
- 10 square feet (longer sides)
- 6 square feet (shorter sides)
- 15 square feet (top)
This results in a total painted area of 31 square feet, which is the amount Bob will need to cover.