Final answer:
To find the area of the wall that needs to be painted, subtract the area of the wall behind the stage from the area of the entire auditorium.
Step-by-step explanation:
To find the area of the wall that needs to be painted, we first calculate the area of the entire auditorium, which is the length multiplied by the width:
Area of auditorium = length × width = 40m × 32m = 1280m²
Next, we subtract the area of the wall behind the stage from the area of the auditorium:
Area of wall to be painted = Area of auditorium - Area of wall behind stage = 1280m² - (22m × 16m) = 1,280m² - 352m² = 928m²Therefore, the area of the wall that needs to be painted is 928 square meters.