Final answer:
To find the total area to be painted in the room, the wall area (603 square feet) and ceiling area (270 square feet) are calculated separately and then added together for one coat, resulting in 873 square feet. This total is then doubled for two coats, giving a final area of 1746 square feet.
Step-by-step explanation:
To calculate the total area that needs to be painted for a room measuring 20 feet by 13 feet 6 inches with a 9 foot ceiling, we need to find the surface area of the walls and ceiling. Since there are two coats of paint needed, we will calculate the single coat area first and then double that for the final area.
Firstly, convert 13 feet 6 inches to feet by dividing 6 inches by 12, giving us 13.5 feet. Next, calculate the area of each wall by multiplying their height by their width. There are two sets of opposite walls: one set is 20 feet wide and the other set is 13.5 feet wide. Each set has two walls and both are 9 feet high.
Area of two longer walls = 2 × (20 feet × 9 feet) = 360 square feet
Area of two shorter walls = 2 × (13.5 feet × 9 feet) = 243 square feet
Total wall area = 360 square feet + 243 square feet = 603 square feet
Next, calculate the ceiling area, which is a rectangle with a length of 20 feet and width of 13.5 feet.
Ceiling area = 20 feet × 13.5 feet = 270 square feet
To find the total area for one coat of paint, add the wall area and ceiling area together.
Total area for one coat = 603 square feet + 270 square feet = 873 square feet
Since two coats are needed, we multiply the total area for one coat by two.
Total area for two coats = 873 square feet × 2 = 1746 square feet